class: center, middle, inverse, title-slide # Feature-based Time Series Forecasting ## Why R? 2021 ### Thiyanga S. Talagala ### 2021-12-10 --- class: center, middle background-image: url(img/shopping.jpg) background-size: contain class: center, top, inverse --- background-image: url(img/bananas.jpg) class: center, top, inverse --- ## Sales data .pull-left[ Data from June, 2011 to November, 2021 ``` # A tsibble: 126 x 2 [1M] Time Sales <mth> <dbl> 1 2011 Jun 2317 2 2011 Jul 2265 3 2011 Aug 2842 4 2011 Sep 2485 5 2011 Oct 2904 6 2011 Nov 2782. 7 2011 Dec 2587 8 2012 Jan 2734. 9 2012 Feb 2390. 10 2012 Mar 2657 # … with 116 more rows ``` ] .pull-right[ <!-- --> ] --- ## Sales data .pull-left[ Data from June, 2011 to November, 2021 ``` # A tsibble: 126 x 2 [1M] Time Sales <mth> <dbl> 1 2011 Jun 2317 2 2011 Jul 2265 3 2011 Aug 2842 4 2011 Sep 2485 5 2011 Oct 2904 6 2011 Nov 2782. 7 2011 Dec 2587 8 2012 Jan 2734. 9 2012 Feb 2390. 10 2012 Mar 2657 # … with 116 more rows ``` ] .pull-right[ <!-- --> ] --- ## Sales data .pull-left[ <!-- --> ] -- .pull-right[ - **How much** will you sell over the next 12 months? - **How much** do we need to produce and **when**? ] --- ### What might happen during a typical model building process? <!-- --> --- ### What might happen during a typical model building process? <!-- --> --- ### What might happen during a typical model building process? <!-- --> --- ### What might happen during a typical model building process? <!-- --> --- ### What might happen during a typical model building process? <!-- --> --- ### What might happen during a typical model building process? <!-- --> --- background-image: url(img/supermarket.jpg) class: center, top, inverse --- background-image: url(img/supermarket.jpg) class: center, top, inverse .full-width[.content-box-blue[Multiple products]] --- background-image: url(img/globe.jpg) class: center, top, inverse .full-width[.content-box-blue[Multiple products across many warehouses]] --- ## Number of series: 1 <!-- --> --- ## Number of series: 2 <!-- --> --- ## Number of series: 3 <!-- --> --- ## Number of series: 10 <!-- --> --- ## Number of series: More than 100 <!-- --> --- class: center, middle, inverse #How to forecast large number of univariate time series? --- ## Aggregate selection rule <!-- --> --- ## Individual model building <!-- --> --- ## Individual model building .pull-left[ <!-- --> ] -- .pull-right[ <!-- --> ] -- .full-width[.content-box-green[.justify-center[How to choose the right forecasting techniques?]]] --- class: inverse background-image: url(img/rice1.png) background-size: contain --- class: inverse background-image: url(img/rice2.png) background-size: contain --- #### Time series <!-- --> --- <!-- --> --- #### Time series and their best forecasting method <!-- --> --- background-image: url(img/tukey.jpeg) background-size: 200px background-position: 100% 6% # Time series features - **Cognostics**: **Co**mputer-aided dia**gnostics** (John W. Tukey, 1985) - Characteristics of time series - Summary measures of time series **Basic Principle** - Transform a given time series `\(y=\{y_1, y_2, \cdots, y_n\}\)` into a feature vector `\(F = (f_1(y), f_2(y), \cdots, f_p(y))'\)`. --- .pull-left[ #### Time-domain representation <!-- --> ] -- .pull-right[ #### Time series features - Strength of trend - Strength of seasonality ``` # A tibble: 6 × 3 trend seasonality id <dbl> <dbl> <chr> 1 0.995 0 N0001 2 0.591 0 N0633 3 0.961 0 N0625 4 0.178 0 N0645 5 0.251 0.906 N1912 6 0.968 0.927 N2012 ``` ] --- .pull-left[ <!-- --> ] .pull-right[ `$$y_t = T_t + S_t + R_t$$` `$$F_T = max \left(0, 1 - \frac{Var(R_t)}{Var(T_t + R_t)} \right)$$` `$$F_S = max \left(0, 1 - \frac{Var(R_t)}{Var(S_t + R_t)} \right)$$` ] --- .pull-left[ #### Time-domain representation <!-- --> ] -- .pull-right[ #### Feature-domain representation <!-- --> ] --- ## Examples of time series features .pull-left[ - length - strength of trend - strength of seasonality - lag-1 autocorrelation - spectral entropy - proportion of zeros - spikiness ] .pull-right[ - curvature - linearity - stability - number of peaks - parameter estimates of Holt-Winters' additive method - unit root test statistics ] --- class: center, middle # Feature-based time series forecasting --- class: inverse, center, middle background-image: url(img/f1.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f2.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f3.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f4.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f5.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f6.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f7.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f8.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f9.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f10.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f11.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f12.png) background-size: contain --- class: inverse, center, middle background-image: url(img/f13.png) background-size: contain --- ### FFORMS: **F**eature-based **FOR**ecast **M**odel **S**election .pull-left[ seer (magic ball) <img src="img/seer.png" width="50%" /> ```r install.packages("seer") #library(devtools) #install_github("thiyangt/seer") library(seer) ``` ] -- .pull-right[ Acropolis Museum, Athens, Greece <img src="img/greece.JPG" width="60%" /> ] --- ## seer package **Training set** ```r library(Mcomp) data(M1) yearly_m1 <- subset(M1, "yearly") yearly_m1 ``` ``` M-Competition data: 181 YEARLY time series Type of data Period DEMOGR INDUST MACRO1 MACRO2 MICRO1 MICRO2 MICRO3 YEARLY 30 35 30 29 16 29 12 ``` **Test set** ```r data(M3) yearly_m3 <- subset(M3, "yearly") m3y <- M3[1:2] m3y ``` ``` Type of data Period MICRO YEARLY 2 ``` --- ## seer package: `cal_features` ``` # A tibble: 181 × 25 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> 1 0.442 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603 2 0.363 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272 3 0.379 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172 4 0.363 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396 5 0.156 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113 6 0.441 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385 7 0.118 0 0 0.943 0.975 4.95e-6 2.94 0.391 0.0868 8 0.357 0 0 0.949 0.978 2.39e-6 3.11 -0.360 0.220 9 0.698 0 0 0.931 0.983 5.09e-6 2.74 0.381 0.198 10 0.435 0.0188 1.05 0.987 0.956 8.44e-6 4.70 -1.57 0.445 # … with 171 more rows, and 16 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, # diff2y_acf1 <dbl>, y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, # nonlinearity <dbl>, lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>, # y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, beta <dbl> ``` --- ## seer package: `fcast_accuracy` ```r accuracy_m1 <- fcast_accuracy(tslist=yearly_m1, models= c("arima","ets","rw","rwd", "theta", "nn"), database ="M1", cal_MASE, h=6, length_out = 1, fcast_save = TRUE) accuracy_m1 ``` ``` $accuracy arima ets rw rwd theta nn YAF2 10.52761210 10.31902909 13.5242826 10.5276121 12.0883746 11.8068095 YAF3 5.71386709 7.70440875 7.7894900 5.2259645 6.2254631 6.7007464 YAF4 8.63359043 8.09141559 11.5563254 8.4401052 9.9527425 10.7843266 YAF5 2.94027818 3.55921826 3.8159137 2.0593759 3.3634957 5.6131570 YAF6 10.12704721 10.20979344 13.1853523 11.8011284 11.9567016 12.0373937 YAF7 5.54339312 3.59967847 7.7707855 5.6992117 6.7834130 7.9261552 YAF8 7.60049192 11.10059289 11.1004919 7.6004919 9.3402119 10.6301534 YAF9 6.84308990 10.34324932 10.3430899 6.8430899 8.7991545 2.9157838 YAF10 5.86529331 9.25760811 9.2574869 5.8652933 7.5936209 8.6301377 YAF11 1.23793267 1.63301650 0.8753143 1.2379327 0.8214250 1.3109233 YAF12 3.40072568 4.52700282 2.5459640 2.1821816 1.9823345 1.9073483 YAF13 3.92372789 4.57608592 13.8754910 10.4707713 12.3532647 5.0295784 YAF14 8.49703094 9.47041582 10.3081214 8.6474142 9.5188299 10.2273204 YAF15 4.36913758 1.96868734 2.2912143 4.3691376 3.4009541 2.2634298 YAF16 7.34633345 9.08427659 9.0842269 6.2573504 7.4701031 8.8633042 YAF17 1.20990669 1.11067633 2.4250935 1.2099067 0.6561892 0.5684528 YAM1 2.54683126 2.53579067 2.5468313 1.6143928 2.1537059 3.4165965 YAM2 4.25524677 4.90899829 5.0623649 3.0576324 4.0734154 7.6919078 YAM3 6.05683571 5.89014664 8.1461278 6.0568357 7.0407755 8.0638885 YAM4 1.19998236 1.20003498 1.1999824 2.2359992 1.7840516 1.4799302 YAM5 3.31794454 2.83506356 2.8350440 1.0886081 1.7970424 2.8181703 YAM6 1.47552380 1.16753611 2.0997057 1.4755238 0.4562984 0.3293274 YAM7 2.83313760 2.67867100 5.8312493 8.1481252 7.0284151 7.1772403 YAM8 1.80107203 1.80141438 0.8839303 1.5957746 0.8706297 1.5898897 YAM10 2.19130032 0.69600689 0.2018244 0.4169883 0.3389725 0.7786616 YAM11 1.27865397 1.08969165 1.0896916 1.1543688 1.1566558 1.3824187 YAM12 1.59902131 1.21865607 1.2372645 1.2561412 1.1928689 1.3384161 YAM13 1.21864476 1.27404616 1.3859609 1.4067800 1.2664949 1.2263810 YAM14 1.57735714 1.57730115 1.5773571 0.5354010 1.1179100 1.7157638 YAM15 1.36239732 1.34961897 1.3623973 0.9192394 1.0313569 1.0127746 YAM16 2.74727838 2.95328269 2.7472784 2.4252260 3.2005197 2.8531585 YAM17 1.93192037 1.33645073 1.9319204 1.4846981 1.0876595 2.8024334 YAM18 1.81862167 1.81446336 3.4247628 1.8186217 2.4413399 1.9123879 YAM19 6.40541465 6.23091817 5.7614896 4.8690052 6.5556919 6.2108880 YAM20 0.87905348 0.87905260 0.8790535 0.8586165 0.8152457 3.4579095 YAM21 7.15484924 6.82442652 4.8888714 4.3456730 6.4407452 9.2120612 YAM22 1.99880648 1.23012771 1.2301178 0.8267946 1.2035729 2.0862838 YAM23 2.16308213 1.34679107 3.0789946 0.6116472 1.5769453 1.4343883 YAM24 2.96436564 2.83000074 4.5744272 2.9643656 3.7487062 4.1406176 YAM25 2.69644785 2.67339693 3.0070651 2.6964478 2.4954923 3.3530524 YAM26 5.10341668 6.12705992 6.1270879 5.1034167 5.5170900 6.7712752 YAM27 5.99145614 6.42086150 12.1183489 9.0463863 10.6348135 9.0662920 YAM28 2.27016299 2.32372771 8.2290301 4.8541543 6.6341227 3.2816350 YAM29 0.67800479 1.60335901 1.6034519 1.9104025 1.6172736 1.9511697 YAM30 2.58534179 3.71125046 3.5087245 2.5853418 3.1671978 5.9682956 YAB1 8.57037535 10.70713708 10.7070353 8.5703754 9.8500447 7.2296564 YAB2 53.27096930 54.68724109 54.4284068 52.1369215 53.7358663 54.6349113 YAB3 1.64307480 2.27349166 3.0010425 1.6430748 2.1711209 3.8354909 YAB4 0.93073823 0.75496556 0.9307382 1.6754800 0.9155919 2.0334837 YAB5 1.79037148 1.87840385 2.8761107 1.7903715 2.1658297 2.8807747 YAB6 1.58852915 1.41627949 1.9834491 1.6443917 1.5904213 2.1727283 YAB7 2.98751826 2.75541598 4.0673624 2.8001476 3.0138617 4.0506544 YAB8 1.59886537 1.63856327 0.6526522 0.7004366 2.5103844 0.7192339 YAB9 1.82402405 1.73629494 2.9786076 1.8240240 1.9264377 7.6339968 YAB10 0.25387047 0.25387047 0.2538705 2.0162514 1.0321389 0.5193442 YAB11 2.62445201 2.62468833 2.6244520 3.3653055 2.8741078 2.6916586 YAB12 0.61364395 0.63009457 0.6464594 0.7666961 0.6783314 0.8289168 YAI1 0.84038360 0.65794982 2.4409748 0.8403836 1.1291816 6.4941538 YAI2 1.84706443 1.84692642 1.8470644 2.5850523 2.0289561 1.4927687 YAI3 2.46630104 2.73506357 1.7091554 1.6338435 2.7354415 2.7093649 YAI4 4.17243587 3.90943669 4.0185403 4.3598451 4.1138835 2.0781165 YAI5 0.79843574 1.08460772 1.0845339 1.1751358 1.1500846 0.9661339 YAI6 0.81682199 0.44234378 4.6295839 1.9245221 3.2872842 1.9201008 YAI7 1.88362389 5.42176745 5.4217973 3.3847504 4.4034704 3.9364002 YAI8 1.56600461 1.75939237 1.5660046 0.5173834 1.3794358 3.2372638 YAI9 5.50159241 6.12078892 9.0015924 5.5015924 7.2815951 6.1138795 YAI10 2.28432579 2.72782233 7.2439705 3.8545873 5.6000909 6.6908678 YAI11 1.53760361 3.63482919 3.5435294 1.5376036 2.8580679 1.9789534 YAI12 1.53626791 1.74543256 2.5933111 1.4435320 1.5757490 1.5732691 YAI13 17.90825719 13.41583616 2.6542728 2.1226881 1.9267821 17.9644019 YAI14 4.55571912 16.14304858 16.1427115 12.6595897 14.6280621 11.8211025 YAI15 3.42245954 3.14626860 1.5676208 3.4224595 2.4759230 4.6992606 YAI16 0.67056431 2.07362376 3.0566182 0.8713338 1.4797262 2.6493381 YAI17 1.69685836 1.27346296 1.2732801 1.6968584 0.9225801 1.8614838 YAI18 4.07161189 4.50073441 4.0716119 2.9454867 4.0627721 4.9333630 YAI19 44.03458333 44.03456109 44.0345833 42.9200139 43.3436506 44.0390499 YAI20 4.21540729 4.32174496 4.2154073 3.6343806 3.8946519 5.4652408 YAI21 2.27016299 2.32372771 8.2290301 4.8541543 6.6341227 3.4590636 YAI22 12.74831543 14.06783534 14.0679075 12.7483154 13.2709173 12.8550482 YAI23 1.04802743 1.01808062 1.0112591 1.1989196 1.0408049 1.4107661 YAI24 7.80688378 4.25960550 10.7834747 7.8068838 9.4208195 9.1620224 YAI25 1.36335131 3.37963810 1.3633513 2.4285612 1.9314515 1.9435777 YAI26 2.90684275 1.41232459 3.1464454 3.0722157 2.5926588 3.2044882 YAI27 4.82774274 4.04034060 3.3165831 2.4508170 2.6292081 2.9957106 YAI28 2.81591360 2.60940689 0.8899578 2.8159136 1.2677723 0.9818791 YAI29 2.73203531 2.52163607 4.5003969 2.7320353 3.4704948 5.0134988 YAI30 2.70743534 1.98713585 0.8006466 2.7074353 1.2919824 8.4873527 YAI31 1.93668578 1.93658045 1.9366858 1.0538813 1.1340969 1.5621517 YAI32 1.64102564 1.64102563 1.6410256 2.8974359 2.1942959 1.6511092 YAI33 0.82972321 0.81973114 2.6306955 3.4546695 1.0279601 2.4681336 YAI34 2.64331541 4.93253399 4.9013799 2.6433154 3.9400377 4.2870724 YAI35 2.04506821 2.04508521 1.8968284 1.7087096 1.7703051 1.7308913 YAG1 2.54933692 3.93993558 6.0493369 2.5493369 4.4394260 1.9584652 YAG2 2.25948229 2.25956650 2.2594823 0.3423751 1.4528729 1.1854464 YAG3 0.98960446 1.00076226 7.1574604 3.8465766 5.4880636 4.4185056 YAG4 1.07910908 0.87360541 1.0791091 1.8688676 1.5607948 6.5965603 YAG5 1.09289617 1.09324964 5.6830601 2.1830601 3.9854571 4.5636685 YAG6 4.47729529 4.74161597 4.4772953 2.2487593 3.3830335 0.9636836 YAG7 2.91200265 0.90399103 0.6691450 0.6301115 0.7875174 21.5712121 YAG8 5.98821568 4.11857241 4.1184296 3.0727506 3.9478542 4.3971866 YAG9 4.76736975 2.47961651 2.4795082 1.9057377 2.4792548 5.4494824 YAG10 0.85157842 3.77163176 3.7715222 0.8515784 2.1833841 2.5447144 YAG11 3.48670255 3.87732073 6.9867025 3.4867025 5.2700112 4.7149722 YAG12 1.57899998 3.74259388 3.7425069 1.5790000 2.9434567 0.9560012 YAG13 4.55048752 4.67900184 7.6195488 4.5504875 6.0815371 8.5040774 YAG14 0.97375938 0.97374287 0.6249995 0.6290548 1.6335376 0.6249077 YAG15 2.84432185 3.61770430 4.9858761 2.8443219 4.0340822 6.1942469 YAG16 3.90624211 4.47082581 7.3520732 3.9062421 5.7936672 5.2408557 YAG17 2.33788465 2.33795639 2.3378847 1.3403135 1.7135377 3.8010257 YAG18 2.77006853 8.15865543 8.1585341 5.3771067 6.8449620 8.0208444 YAG19 6.49027424 5.50917632 10.2331080 7.1043093 8.6425883 9.9985272 YAG20 0.86339916 0.98251744 5.4048706 1.9815194 3.7120204 2.5766310 YAG21 2.99541982 3.69578504 5.7386631 2.9954198 4.5137038 3.2930270 YAG22 0.59876543 1.05473947 3.9753086 0.5987654 2.2399980 1.6066154 YAG23 0.56262386 0.60126910 3.4708680 0.5626239 1.6985848 2.7076239 YAG24 2.08003772 2.26928289 5.3283782 1.8478986 3.5530722 4.4606104 YAG25 1.87950000 3.08035277 5.3146852 1.8795000 3.6864128 1.5091572 YAG26 0.62414781 0.65390173 5.0069444 1.6527778 3.3227839 3.9277121 YAG27 3.09992000 2.31252467 6.5999200 3.0999200 4.9475728 1.1173714 YAG28 0.86030991 0.88503436 4.2882126 0.8603099 2.6021672 4.2174425 YAG29 0.07074949 0.72735092 6.0100303 2.5100303 4.3715168 2.2272104 YAG30 0.46669000 1.54732972 7.3499300 3.8499300 5.6875926 2.6264818 YAC1 1.40139123 2.27678150 4.9013912 1.4013912 3.2377302 0.2217141 YAC2 1.64788713 3.20306204 4.5601376 1.6478871 3.2896412 2.9754993 YAC3 0.72655978 0.82264941 6.1185606 2.6185606 4.3172360 6.4017409 YAC4 1.09723495 0.86703152 5.8233514 2.3695976 4.1916317 0.6391978 YAC5 2.93115557 3.94951167 5.7995318 2.9311556 4.5297922 2.4094155 YAC6 0.54893870 0.48753454 0.5489387 1.2278225 0.7583333 0.7883657 YAC7 1.86323404 3.06635102 3.9520638 1.8632340 3.1546103 2.5523373 YAC8 1.25783550 0.65667255 7.2033890 4.7683241 5.9336542 6.3504580 YAC9 0.87350898 0.97202279 5.3971497 2.1095250 3.7566096 1.5880075 YAC10 2.58773523 4.61761196 4.6175333 2.5877352 3.8742645 1.2397568 YAC11 6.84463515 7.97419436 10.3446352 6.8446352 8.7810648 8.3527813 YAC12 1.82866492 2.22982145 5.3286649 1.8286649 3.6183147 2.5251134 YAC13 5.68734181 4.50676209 5.6873418 4.0336516 5.2182008 7.5433740 YAC14 2.57222049 2.13714471 2.1371447 1.3277470 1.8649361 3.1800877 YAC15 3.86759191 3.86729179 9.1831685 5.6831685 7.4389747 6.1697503 YAC16 0.90349483 1.18178224 0.9034948 0.7867049 0.9457474 2.0424056 YAC17 5.26498644 5.80308181 7.0853978 5.2649864 6.4634574 8.6916943 YAC18 1.87279661 1.64035878 5.3727966 1.8727966 3.6768294 2.4838477 YAC19 0.84371342 2.30643885 2.2918438 0.8437134 1.6132961 1.2923016 YAC20 0.38731474 0.09952735 3.4110916 0.1356388 1.7091136 2.4901694 YAC21 1.95227324 1.86819987 5.0995297 1.9522732 3.4146410 4.5927079 YAC22 2.71347047 2.64481865 8.1040215 4.6040215 6.3975309 5.4524715 YAC23 1.80620861 1.10672591 4.9005795 1.8062086 3.2294536 4.9645296 YAC24 1.30648607 2.96986108 2.9697456 0.4649762 2.0995904 1.4028911 YAC25 2.96701565 2.85465812 7.7948624 4.2948624 6.0634344 5.1079922 YAC26 4.42214970 7.35639284 7.3562814 4.4221497 6.1816126 1.1440488 YAC27 0.99068519 0.74770121 5.5295741 2.2925370 3.8911075 2.2404818 YAC28 3.47254800 3.78016924 6.6161036 3.4725480 4.8511688 6.2368434 YAC29 1.08984505 3.14643861 3.1464601 1.0898451 1.7003076 3.1062555 YAD1 5.32880508 5.32899343 4.1338865 4.3937118 5.6129407 5.5596425 YAD2 4.16840894 4.15583328 5.9936273 2.9568189 4.4446085 5.7373967 YAD3 0.42340177 0.77174669 0.4314063 0.5811338 0.3718245 1.5611735 YAD4 1.74576093 1.74547087 0.8071617 0.2615587 1.0219153 2.0237081 YAD5 1.01524242 1.77444600 1.0152424 1.2161994 1.9261107 2.7220973 YAD6 0.97887135 0.96238162 2.2619400 2.6515504 1.0119491 0.6661049 YAD7 0.93418975 0.80119406 2.2267709 2.5916119 0.9727596 0.5569053 YAD8 0.95015958 0.89533123 2.2338180 2.6090432 0.9862256 0.6025862 YAD9 1.60601348 1.72683440 0.7662312 0.9544032 1.9282141 2.6155298 YAD10 1.79944413 1.80838059 0.9992112 1.2296460 1.9809520 2.8222610 YAD11 3.63702912 3.63726892 2.8391202 2.3543440 3.9637990 2.9444382 YAD12 0.89467778 0.94672217 0.8946778 1.3219889 0.4582498 0.8068597 YAD13 1.02927451 0.82352941 1.0292745 1.1910392 0.8124387 0.8851248 YAD14 1.70683124 2.96006979 3.0763781 3.2308297 3.0296397 1.5755227 YAD15 9.08651852 9.08666668 9.0865185 7.1420741 8.0755267 9.1451736 YAD16 0.41025641 0.41025641 1.0255179 1.8332103 0.4145299 0.4089155 YAD17 8.25973952 6.53546777 6.3776383 5.9265859 6.2885599 7.0298965 YAD18 7.23138746 6.65853431 6.5105897 6.8439231 6.8157312 6.9463681 YAD19 5.55066667 5.55673526 5.0425139 5.0911023 5.7691484 5.1833503 YAD20 1.54227823 8.52836495 8.5281653 5.0563911 6.9132895 6.9075536 YAD21 1.41039755 1.45990904 2.5926606 0.9073394 0.7864160 1.6429041 YAD22 2.55734886 1.55287633 1.4130735 0.9306174 1.5983157 2.6160230 YAD23 2.74067749 1.60152285 1.4588519 0.9561418 1.6396497 0.8386533 YAD24 0.55143439 1.17437947 0.5514344 0.6494659 0.7257569 1.3121129 YAD25 1.47668822 1.46966525 3.3810704 0.4404813 1.5987701 1.5747937 YAD26 0.56735469 1.20168108 0.5673547 0.6549806 0.7623183 1.5479130 YAD27 4.58130172 3.02046450 3.0202983 1.8067608 2.7016179 15.0480535 YAD28 6.55007236 5.16689524 5.1667519 4.2536441 4.8230043 5.3594850 YAD29 1.44673203 0.98500034 1.1459238 1.1694246 0.9875650 1.3376342 YAD30 3.92046205 3.91847882 3.9204620 3.3983498 3.5601419 3.6605486 $ARIMA YAF2 YAF3 "ARIMA(0,1,0) with drift" "ARIMA(0,1,1) with drift" YAF4 YAF5 "ARIMA(0,1,2) with drift" "ARIMA(1,1,0) with drift" YAF6 YAF7 "ARIMA(0,1,1) with drift" "ARIMA(1,1,0) with drift" YAF8 YAF9 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAF10 YAF11 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAF12 YAF13 "ARIMA(0,2,1)" "ARIMA(0,2,1)" YAF14 YAF15 "ARIMA(2,2,0)" "ARIMA(0,1,0) with drift" YAF16 YAF17 "ARIMA(0,2,0)" "ARIMA(0,1,0) with drift" YAM1 YAM2 "ARIMA(0,1,0)" "ARIMA(0,1,1) with drift" YAM3 YAM4 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0)" YAM5 YAM6 "ARIMA(0,1,1)" "ARIMA(0,1,0) with drift" YAM7 YAM8 "ARIMA(0,2,0)" "ARIMA(0,0,0) with non-zero mean" YAM10 YAM11 "ARIMA(2,0,0) with non-zero mean" "ARIMA(1,0,0) with non-zero mean" YAM12 YAM13 "ARIMA(0,0,1) with non-zero mean" "ARIMA(0,0,0) with non-zero mean" YAM14 YAM15 "ARIMA(0,1,0)" "ARIMA(0,1,0)" YAM16 YAM17 "ARIMA(0,1,0)" "ARIMA(0,1,0)" YAM18 YAM19 "ARIMA(0,1,0) with drift" "ARIMA(2,0,1) with non-zero mean" YAM20 YAM21 "ARIMA(0,1,0)" "ARIMA(2,0,0) with non-zero mean" YAM22 YAM23 "ARIMA(2,0,0) with non-zero mean" "ARIMA(0,2,1)" YAM24 YAM25 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAM26 YAM27 "ARIMA(0,1,0) with drift" "ARIMA(0,2,1)" YAM28 YAM29 "ARIMA(0,2,1)" "ARIMA(1,0,0) with non-zero mean" YAM30 YAB1 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAB2 YAB3 "ARIMA(1,1,0)" "ARIMA(0,1,0) with drift" YAB4 YAB5 "ARIMA(0,1,0)" "ARIMA(0,1,0) with drift" YAB6 YAB7 "ARIMA(0,1,2) with drift" "ARIMA(0,2,0)" YAB8 YAB9 "ARIMA(0,0,0) with non-zero mean" "ARIMA(0,1,0) with drift" YAB10 YAB11 "ARIMA(0,1,0)" "ARIMA(0,1,0)" YAB12 YAI1 "ARIMA(2,1,0)" "ARIMA(0,1,0) with drift" YAI2 YAI3 "ARIMA(0,1,0)" "ARIMA(0,0,1) with non-zero mean" YAI4 YAI5 "ARIMA(1,1,0)" "ARIMA(1,0,0) with non-zero mean" YAI6 YAI7 "ARIMA(0,2,1)" "ARIMA(0,2,1)" YAI8 YAI9 "ARIMA(0,1,0)" "ARIMA(0,1,0) with drift" YAI10 YAI11 "ARIMA(0,2,1)" "ARIMA(0,1,0) with drift" YAI12 YAI13 "ARIMA(0,2,0)" "ARIMA(0,2,0)" YAI14 YAI15 "ARIMA(0,2,0)" "ARIMA(0,1,0) with drift" YAI16 YAI17 "ARIMA(0,1,1) with drift" "ARIMA(0,1,0) with drift" YAI18 YAI19 "ARIMA(0,1,0)" "ARIMA(0,1,0)" YAI20 YAI21 "ARIMA(0,1,0)" "ARIMA(0,2,1)" YAI22 YAI23 "ARIMA(0,1,0) with drift" "ARIMA(0,0,1) with non-zero mean" YAI24 YAI25 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0)" YAI26 YAI27 "ARIMA(1,0,0) with non-zero mean" "ARIMA(1,2,0)" YAI28 YAI29 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAI30 YAI31 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0)" YAI32 YAI33 "ARIMA(0,1,0)" "ARIMA(0,0,0) with non-zero mean" YAI34 YAI35 "ARIMA(0,1,0) with drift" "ARIMA(0,0,0) with non-zero mean" YAG1 YAG2 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0)" YAG3 YAG4 "ARIMA(1,2,0)" "ARIMA(0,1,0)" YAG5 YAG6 "ARIMA(0,2,0)" "ARIMA(0,1,0)" YAG7 YAG8 "ARIMA(1,0,0) with non-zero mean" "ARIMA(2,0,0) with non-zero mean" YAG9 YAG10 "ARIMA(2,0,0) with non-zero mean" "ARIMA(0,1,0) with drift" YAG11 YAG12 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAG13 YAG14 "ARIMA(0,1,0) with drift" "ARIMA(0,0,0) with non-zero mean" YAG15 YAG16 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAG17 YAG18 "ARIMA(0,1,0)" "ARIMA(0,2,0)" YAG19 YAG20 "ARIMA(0,2,0)" "ARIMA(0,2,1)" YAG21 YAG22 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAG23 YAG24 "ARIMA(0,1,0) with drift" "ARIMA(3,2,0)" YAG25 YAG26 "ARIMA(0,1,0) with drift" "ARIMA(0,2,1)" YAG27 YAG28 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAG29 YAG30 "ARIMA(0,2,0)" "ARIMA(0,2,0)" YAC1 YAC2 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAC3 YAC4 "ARIMA(0,2,1)" "ARIMA(1,2,0)" YAC5 YAC6 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0)" YAC7 YAC8 "ARIMA(0,1,0) with drift" "ARIMA(0,2,0)" YAC9 YAC10 "ARIMA(0,2,0)" "ARIMA(0,1,0) with drift" YAC11 YAC12 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAC13 YAC14 "ARIMA(0,1,0)" "ARIMA(2,1,0)" YAC15 YAC16 "ARIMA(0,2,0)" "ARIMA(0,1,0)" YAC17 YAC18 "ARIMA(0,1,0) with drift" "ARIMA(0,1,0) with drift" YAC19 YAC20 "ARIMA(0,1,0) with drift" "ARIMA(0,2,0)" YAC21 YAC22 "ARIMA(0,1,0) with drift" "ARIMA(0,2,1)" YAC23 YAC24 "ARIMA(0,1,0) with drift" "ARIMA(1,1,0)" YAC25 YAC26 "ARIMA(0,2,0)" "ARIMA(0,1,0) with drift" YAC27 YAC28 "ARIMA(0,2,0)" "ARIMA(0,1,0) with drift" YAC29 YAD1 "ARIMA(0,1,0) with drift" "ARIMA(0,0,0) with non-zero mean" YAD2 YAD3 "ARIMA(0,2,1)" "ARIMA(0,1,1) with drift" YAD4 YAD5 "ARIMA(0,0,0) with non-zero mean" "ARIMA(0,1,0)" YAD6 YAD7 "ARIMA(0,1,1)" "ARIMA(0,1,1)" YAD8 YAD9 "ARIMA(0,1,1)" "ARIMA(1,0,1) with non-zero mean" YAD10 YAD11 "ARIMA(0,0,1) with non-zero mean" "ARIMA(0,0,0) with non-zero mean" YAD12 YAD13 "ARIMA(0,1,0)" "ARIMA(0,1,0)" YAD14 YAD15 "ARIMA(1,0,0) with non-zero mean" "ARIMA(0,1,0)" YAD16 YAD17 "ARIMA(0,0,0) with non-zero mean" "ARIMA(1,0,0) with non-zero mean" YAD18 YAD19 "ARIMA(0,0,0) with non-zero mean" "ARIMA(0,0,1) with non-zero mean" YAD20 YAD21 "ARIMA(0,2,0)" "ARIMA(0,2,0)" YAD22 YAD23 "ARIMA(1,0,0) with non-zero mean" "ARIMA(0,0,1) with non-zero mean" YAD24 YAD25 "ARIMA(0,1,0)" "ARIMA(0,2,0)" YAD26 YAD27 "ARIMA(0,1,0)" "ARIMA(1,0,0) with non-zero mean" YAD28 YAD29 "ARIMA(1,0,0) with non-zero mean" "ARIMA(0,0,1) with non-zero mean" YAD30 "ARIMA(0,1,0)" $ETS YAF2 YAF3 YAF4 YAF5 YAF6 "ETS(A,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" YAF7 YAF8 YAF9 YAF10 YAF11 "ETS(M,A,N)" "ETS(M,N,N)" "ETS(A,N,N)" "ETS(M,N,N)" "ETS(M,A,N)" YAF12 YAF13 YAF14 YAF15 YAF16 "ETS(A,A,N)" "ETS(A,A,N)" "ETS(M,A,N)" "ETS(A,A,N)" "ETS(M,N,N)" YAF17 YAM1 YAM2 YAM3 YAM4 "ETS(M,A,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(A,Ad,N)" "ETS(A,N,N)" YAM5 YAM6 YAM7 YAM8 YAM10 "ETS(M,N,N)" "ETS(M,A,N)" "ETS(A,A,N)" "ETS(A,N,N)" "ETS(M,A,N)" YAM11 YAM12 YAM13 YAM14 YAM15 "ETS(M,N,N)" "ETS(M,N,N)" "ETS(M,N,N)" "ETS(A,N,N)" "ETS(M,N,N)" YAM16 YAM17 YAM18 YAM19 YAM20 "ETS(M,N,N)" "ETS(M,N,N)" "ETS(A,A,N)" "ETS(A,N,N)" "ETS(A,N,N)" YAM21 YAM22 YAM23 YAM24 YAM25 "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" YAM26 YAM27 YAM28 YAM29 YAM30 "ETS(M,N,N)" "ETS(A,A,N)" "ETS(M,A,N)" "ETS(M,N,N)" "ETS(M,A,N)" YAB1 YAB2 YAB3 YAB4 YAB5 "ETS(A,N,N)" "ETS(M,N,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(A,A,N)" YAB6 YAB7 YAB8 YAB9 YAB10 "ETS(M,A,N)" "ETS(A,A,N)" "ETS(M,N,N)" "ETS(A,A,N)" "ETS(A,N,N)" YAB11 YAB12 YAI1 YAI2 YAI3 "ETS(A,N,N)" "ETS(A,A,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(M,N,N)" YAI4 YAI5 YAI6 YAI7 YAI8 "ETS(M,N,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(M,N,N)" "ETS(A,N,N)" YAI9 YAI10 YAI11 YAI12 YAI13 "ETS(M,A,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(A,A,N)" "ETS(M,A,N)" YAI14 YAI15 YAI16 YAI17 YAI18 "ETS(M,N,N)" "ETS(A,A,N)" "ETS(A,A,N)" "ETS(M,N,N)" "ETS(M,N,N)" YAI19 YAI20 YAI21 YAI22 YAI23 "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(A,N,N)" YAI24 YAI25 YAI26 YAI27 YAI28 "ETS(A,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(A,A,N)" "ETS(A,A,N)" YAI29 YAI30 YAI31 YAI32 YAI33 "ETS(M,A,N)" "ETS(A,A,N)" "ETS(A,N,N)" "ETS(A,N,N)" "ETS(A,N,N)" YAI34 YAI35 YAG1 YAG2 YAG3 "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(A,A,N)" YAG4 YAG5 YAG6 YAG7 YAG8 "ETS(M,N,N)" "ETS(A,A,N)" "ETS(M,N,N)" "ETS(M,N,N)" "ETS(A,N,N)" YAG9 YAG10 YAG11 YAG12 YAG13 "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(M,A,N)" YAG14 YAG15 YAG16 YAG17 YAG18 "ETS(M,N,N)" "ETS(A,A,N)" "ETS(A,A,N)" "ETS(M,N,N)" "ETS(M,N,N)" YAG19 YAG20 YAG21 YAG22 YAG23 "ETS(A,A,N)" "ETS(A,A,N)" "ETS(A,A,N)" "ETS(A,A,N)" "ETS(M,A,N)" YAG24 YAG25 YAG26 YAG27 YAG28 "ETS(M,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(A,A,N)" YAG29 YAG30 YAC1 YAC2 YAC3 "ETS(M,A,N)" "ETS(A,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" YAC4 YAC5 YAC6 YAC7 YAC8 "ETS(M,A,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(A,A,N)" "ETS(A,A,N)" YAC9 YAC10 YAC11 YAC12 YAC13 "ETS(A,A,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(A,A,N)" YAC14 YAC15 YAC16 YAC17 YAC18 "ETS(A,N,N)" "ETS(A,A,N)" "ETS(A,N,N)" "ETS(M,A,N)" "ETS(M,A,N)" YAC19 YAC20 YAC21 YAC22 YAC23 "ETS(M,N,N)" "ETS(M,A,N)" "ETS(A,A,N)" "ETS(M,A,N)" "ETS(M,A,N)" YAC24 YAC25 YAC26 YAC27 YAC28 "ETS(A,N,N)" "ETS(M,A,N)" "ETS(A,N,N)" "ETS(A,A,N)" "ETS(M,A,N)" YAC29 YAD1 YAD2 YAD3 YAD4 "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,Ad,N)" "ETS(A,Ad,N)" "ETS(M,N,N)" YAD5 YAD6 YAD7 YAD8 YAD9 "ETS(A,N,N)" "ETS(M,N,N)" "ETS(M,A,N)" "ETS(M,A,N)" "ETS(A,N,N)" YAD10 YAD11 YAD12 YAD13 YAD14 "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,N,N)" "ETS(M,N,N)" "ETS(A,N,N)" YAD15 YAD16 YAD17 YAD18 YAD19 "ETS(A,N,N)" "ETS(M,N,N)" "ETS(A,N,N)" "ETS(A,N,N)" "ETS(M,N,N)" YAD20 YAD21 YAD22 YAD23 YAD24 "ETS(M,N,N)" "ETS(M,A,N)" "ETS(M,N,N)" "ETS(M,N,N)" "ETS(A,N,N)" YAD25 YAD26 YAD27 YAD28 YAD29 "ETS(M,A,N)" "ETS(M,N,N)" "ETS(A,N,N)" "ETS(M,N,N)" "ETS(M,N,N)" YAD30 "ETS(A,N,N)" $forecasts $forecasts$arima YAF2 YAF3 YAF4 YAF5 YAF6 YAF7 YAF8 YAF9 [1,] 579581.0 390955.9 369704.9 326878.3 21141635 15770.87 904964.3 673803.7 [2,] 605761.9 407325.1 392255.0 366064.9 21677177 16255.32 962222.7 709311.4 [3,] 631942.9 423694.4 408717.0 365288.0 22212720 16905.57 1019481.0 744819.1 [4,] 658123.8 440063.6 425179.1 390109.0 22748262 17466.14 1076739.3 780326.8 [5,] 684304.8 456432.8 441641.1 398533.7 23283804 18075.21 1133997.7 815834.5 [6,] 710485.7 472802.0 458103.2 417460.7 23819346 18658.05 1191256.0 851342.2 YAF10 YAF11 YAF12 YAF13 YAF14 YAF15 YAF16 YAF17 YAM1 [1,] 906621.4 55.13 8963.293 1904976 54652.02 908663.9 1068.0 8.764489 71755 [2,] 951113.7 56.33 9479.587 2098112 52595.04 950829.8 1094.1 8.945009 71755 [3,] 995606.1 57.53 9995.880 2291249 54523.59 992995.7 1120.2 9.125528 71755 [4,] 1040098.5 58.73 10512.173 2484385 56366.94 1035161.6 1146.3 9.306048 71755 [5,] 1084590.9 59.93 11028.467 2677521 55539.93 1077327.5 1172.4 9.486567 71755 [6,] 1129083.2 61.13 11544.760 2870657 57751.48 1119493.4 1198.5 9.667087 71755 YAM2 YAM3 YAM4 YAM5 YAM6 YAM7 YAM8 YAM10 [1,] 635257.8 7089.829 18139 28.87587 2.753552 1774.8 94.18462 70.59584 [2,] 665525.9 7323.188 18139 28.87587 2.766793 1630.2 94.18462 92.62441 [3,] 695794.0 7556.547 18139 28.87587 2.780035 1485.6 94.18462 116.32355 [4,] 726062.0 7789.906 18139 28.87587 2.793276 1341.0 94.18462 135.51812 [5,] 756330.1 8023.265 18139 28.87587 2.806518 1196.4 94.18462 146.59663 [6,] 786598.2 8256.624 18139 28.87587 2.819759 1051.8 94.18462 148.78354 YAM11 YAM12 YAM13 YAM14 YAM15 YAM16 YAM17 YAM18 YAM19 [1,] 19717359 12630014 2725.212 811 770 100.8 175 5773.286 99.55630 [2,] 19172800 12247801 2725.212 811 770 100.8 175 5964.571 95.03239 [3,] 18805626 12247801 2725.212 811 770 100.8 175 6155.857 95.95622 [4,] 18558055 12247801 2725.212 811 770 100.8 175 6347.143 100.24116 [5,] 18391128 12247801 2725.212 811 770 100.8 175 6538.429 100.11698 [6,] 18278576 12247801 2725.212 811 770 100.8 175 6729.714 96.18441 YAM20 YAM21 YAM22 YAM23 YAM24 YAM25 YAM26 YAM27 [1,] 9383 205.5751 95.59372 12671.75 9352.15 11898.3 25885.5 610.7561 [2,] 9383 188.8118 88.46585 13290.51 9654.30 12170.6 26363.0 662.5122 [3,] 9383 177.4192 85.72708 13909.26 9956.45 12442.9 26840.5 714.2684 [4,] 9383 180.7550 86.55871 14528.01 10258.60 12715.2 27318.0 766.0245 [5,] 9383 191.6987 88.42534 15146.77 10560.75 12987.5 27795.5 817.7806 [6,] 9383 197.8305 89.59875 15765.52 10862.90 13259.8 28273.0 869.5367 YAM28 YAM29 YAM30 YAB1 YAB2 YAB3 YAB4 YAB5 [1,] 1318.168 7873.221 76266.65 31148.35 7935.886 621170.9 80389 10547.31 [2,] 1417.335 7736.379 77866.30 32487.70 8124.539 653863.9 80389 10909.63 [3,] 1516.503 7620.631 79465.96 33827.05 8217.978 686556.8 80389 11271.94 [4,] 1615.671 7522.726 81065.61 35166.40 8264.259 719249.8 80389 11634.25 [5,] 1714.838 7439.912 82665.26 36505.75 8287.182 751942.7 80389 11996.56 [6,] 1814.006 7369.864 84264.91 37845.10 8298.536 784635.7 80389 12358.88 YAB6 YAB7 YAB8 YAB9 YAB10 YAB11 YAB12 YAI1 YAI2 [1,] 834.7073 721910 169402.1 250283.4 39098 142157 26748.39 1257.088 39177 [2,] 800.3679 751718 169402.1 270777.7 39098 142157 26454.84 1323.176 39177 [3,] 815.7275 781526 169402.1 291272.1 39098 142157 26733.55 1389.265 39177 [4,] 831.0871 811334 169402.1 311766.5 39098 142157 26638.23 1455.353 39177 [5,] 846.4467 841142 169402.1 332260.8 39098 142157 26596.86 1521.441 39177 [6,] 861.8063 870950 169402.1 352755.2 39098 142157 26668.63 1587.529 39177 YAI3 YAI4 YAI5 YAI6 YAI7 YAI8 YAI9 YAI10 YAI11 [1,] 378.1661 3055.081 697.5569 1938336 22644175 8800.8 290.2 219836.9 662.7529 [2,] 235.6548 3024.749 650.2141 2016812 23488151 8800.8 310.4 227533.8 692.9059 [3,] 235.6548 3036.532 611.8632 2095289 24332126 8800.8 330.6 235230.7 723.0588 [4,] 235.6548 3031.955 580.7964 2173765 25176102 8800.8 350.8 242927.6 753.2118 [5,] 235.6548 3033.733 555.6301 2252241 26020077 8800.8 371.0 250624.5 783.3647 [6,] 235.6548 3033.042 535.2438 2330717 26864053 8800.8 391.2 258321.4 813.5176 YAI12 YAI13 YAI14 YAI15 YAI16 YAI17 YAI18 YAI19 YAI20 [1,] 1524.9 1372.3 1014.2 260.4941 139.2705 1332.518 111.5 38.2 13.936 [2,] 1577.6 1706.2 1218.3 273.8882 146.8112 1392.835 111.5 38.2 13.936 [3,] 1630.3 2040.1 1422.4 287.2824 154.3520 1453.153 111.5 38.2 13.936 [4,] 1683.0 2374.0 1626.5 300.6765 161.8928 1513.471 111.5 38.2 13.936 [5,] 1735.7 2707.9 1830.6 314.0706 169.4335 1573.788 111.5 38.2 13.936 [6,] 1788.4 3041.8 2034.7 327.4647 176.9743 1634.106 111.5 38.2 13.936 YAI21 YAI22 YAI23 YAI24 YAI25 YAI26 YAI27 YAI28 [1,] 1318.168 3205.167 23.00821 135512 56.8 489.3039 4607.910 388.0684 [2,] 1417.335 3293.935 23.29348 139830 56.8 499.4178 4816.082 404.4368 [3,] 1516.503 3382.702 23.29348 144148 56.8 504.7168 5515.399 420.8053 [4,] 1615.671 3471.470 23.29348 148466 56.8 507.4931 5783.759 437.1737 [5,] 1714.838 3560.237 23.29348 152784 56.8 508.9477 6430.265 453.5421 [6,] 1814.006 3649.005 23.29348 157102 56.8 509.7098 6744.964 469.9105 YAI29 YAI30 YAI31 YAI32 YAI33 YAI34 YAI35 YAG1 YAG2 [1,] 150.4105 17.555 6.38 14.2 7.875385 3.46 2.799167 245.9575 52.52 [2,] 156.2211 18.770 6.38 14.2 7.875385 3.58 2.799167 254.3150 52.52 [3,] 162.0316 19.985 6.38 14.2 7.875385 3.70 2.799167 262.6725 52.52 [4,] 167.8421 21.200 6.38 14.2 7.875385 3.82 2.799167 271.0300 52.52 [5,] 173.6526 22.415 6.38 14.2 7.875385 3.94 2.799167 279.3875 52.52 [6,] 179.4632 23.630 6.38 14.2 7.875385 4.06 2.799167 287.7450 52.52 YAG3 YAG4 YAG5 YAG6 YAG7 YAG8 YAG9 YAG10 [1,] 92.61077 11.39 120 107.69 105.60777 186.5144 124.34173 95.52632 [2,] 100.08035 11.39 125 107.69 99.73331 179.1672 118.24181 98.65263 [3,] 107.83204 11.39 130 107.69 96.70411 170.5083 111.05919 101.77895 [4,] 115.41833 11.39 135 107.69 95.14210 162.2249 104.63702 104.90526 [5,] 123.10159 11.39 140 107.69 94.33663 154.8605 99.74308 108.03158 [6,] 130.72801 11.39 145 107.69 93.92129 148.5141 96.47931 111.15789 YAG11 YAG12 YAG13 YAG14 YAG15 YAG16 YAG17 YAG18 YAG19 [1,] 370305.5 113285.7 97293.5 4317.462 31650.58 478816.8 41.42 666 606 [2,] 384055.0 119333.3 100636.0 4317.462 33023.17 497020.7 41.42 734 643 [3,] 397804.5 125381.0 103978.5 4317.462 34395.75 515224.5 41.42 802 680 [4,] 411554.0 131428.7 107321.0 4317.462 35768.33 533428.3 41.42 870 717 [5,] 425303.5 137476.3 110663.5 4317.462 37140.92 551632.2 41.42 938 754 [6,] 439053.0 143524.0 114006.0 4317.462 38513.50 569836.0 41.42 1006 791 YAG20 YAG21 YAG22 YAG23 YAG24 YAG25 YAG26 YAG27 [1,] 877.1081 5.807143 10.48571 137.5071 65.17531 22.85714 11.84057 6.25 [2,] 896.1162 6.014286 10.87143 143.5143 66.95326 23.61429 12.38113 6.50 [3,] 915.1243 6.221429 11.25714 149.5214 69.61589 24.37143 12.92170 6.75 [4,] 934.1324 6.428571 11.64286 155.5286 72.06267 25.12857 13.46226 7.00 [5,] 953.1405 6.635714 12.02857 161.5357 75.01868 25.88571 14.00283 7.25 [6,] 972.1486 6.842857 12.41429 167.5429 77.38557 26.64286 14.54340 7.50 YAG28 YAG29 YAG30 YAC1 YAC2 YAC3 YAC4 YAC5 YAC6 [1,] 7.664286 8.1 4.5 76.5825 28.6575 18.71678 24.50945 98.85917 19.84 [2,] 7.928571 8.5 4.8 78.6550 29.6650 19.73355 27.18523 102.06833 19.84 [3,] 8.192857 8.9 5.1 80.7275 30.6725 20.75033 29.70478 105.27750 19.84 [4,] 8.457143 9.3 5.4 82.8000 31.6800 21.76711 32.31954 108.48667 19.84 [5,] 8.721429 9.7 5.7 84.8725 32.6875 22.78389 34.87627 111.69583 19.84 [6,] 8.985714 10.1 6.0 86.9450 33.6950 23.80066 37.46837 114.90500 19.84 YAC7 YAC8 YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 YAC15 YAC16 [1,] 33.625 27.98 42.67 75474.42 32767.92 54381.67 40034 55177.55 58574 26875 [2,] 34.560 30.33 46.41 77166.83 33675.83 56928.33 40034 54700.53 62860 26875 [3,] 35.495 32.68 50.15 78859.25 34583.75 59475.00 40034 52430.67 67146 26875 [4,] 36.430 35.03 53.89 80551.67 35491.67 62021.67 40034 50173.72 71432 26875 [5,] 37.365 37.38 57.63 82244.08 36399.58 64568.33 40034 49314.62 75718 26875 [6,] 38.300 39.73 61.37 83936.50 37307.50 67115.00 40034 50062.03 80004 26875 YAC17 YAC18 YAC19 YAC20 YAC21 YAC22 YAC23 YAC24 YAC25 [1,] 33610.5 54.46667 32175926 5368 2083.917 2097.978 1743 1891.306 3378 [2,] 34761.0 56.43333 32910651 5595 2150.833 2240.956 1832 1954.300 3591 [3,] 35911.5 58.40000 33645377 5822 2217.750 2383.934 1921 1999.752 3804 [4,] 37062.0 60.36667 34380103 6049 2284.667 2526.912 2010 2032.548 4017 [5,] 38212.5 62.33333 35114828 6276 2351.583 2669.890 2099 2056.211 4230 [6,] 39363.0 64.30000 35849554 6503 2418.500 2812.868 2188 2073.285 4443 YAC26 YAC27 YAC28 YAC29 YAD1 YAD2 YAD3 YAD4 YAD5 [1,] 937.6667 1676 2406.917 2086.083 114.6364 36595.27 297.1427 1917.333 522 [2,] 984.3333 1803 2522.833 2127.167 114.6364 36690.55 298.6082 1917.333 522 [3,] 1031.0000 1930 2638.750 2168.250 114.6364 36785.82 300.0736 1917.333 522 [4,] 1077.6667 2057 2754.667 2209.333 114.6364 36881.10 301.5391 1917.333 522 [5,] 1124.3333 2184 2870.583 2250.417 114.6364 36976.37 303.0045 1917.333 522 [6,] 1171.0000 2311 2986.500 2291.500 114.6364 37071.65 304.4700 1917.333 522 YAD6 YAD7 YAD8 YAD9 YAD10 YAD11 YAD12 YAD13 YAD14 [1,] 449.4026 445.7425 895.012 902.3788 986.8827 3597.4 37.1 39.8 1258.433 [2,] 449.4026 445.7425 895.012 890.9857 965.0326 3597.4 37.1 39.8 1411.542 [3,] 449.4026 445.7425 895.012 895.9207 965.0326 3597.4 37.1 39.8 1490.890 [4,] 449.4026 445.7425 895.012 893.7831 965.0326 3597.4 37.1 39.8 1532.012 [5,] 449.4026 445.7425 895.012 894.7090 965.0326 3597.4 37.1 39.8 1553.323 [6,] 449.4026 445.7425 895.012 894.3080 965.0326 3597.4 37.1 39.8 1564.368 YAD15 YAD16 YAD17 YAD18 YAD19 YAD20 YAD21 YAD22 YAD23 [1,] 23.2 9.411111 403806.5 2.273333 1557784 694 26628 457.5204 441.9463 [2,] 23.2 9.411111 398773.2 2.273333 1550156 749 26815 449.3278 413.4229 [3,] 23.2 9.411111 396017.6 2.273333 1550156 804 27002 444.9918 413.4229 [4,] 23.2 9.411111 394509.0 2.273333 1550156 859 27189 442.6970 413.4229 [5,] 23.2 9.411111 393683.0 2.273333 1550156 914 27376 441.4825 413.4229 [6,] 23.2 9.411111 393230.8 2.273333 1550156 969 27563 440.8397 413.4229 YAD24 YAD25 YAD26 YAD27 YAD28 YAD29 YAD30 [1,] 333594 28179 322404 10468.06 7937.202 55.72755 1016 [2,] 333594 28363 322404 10642.03 8030.728 55.18222 1016 [3,] 333594 28547 322404 10783.43 8106.004 55.18222 1016 [4,] 333594 28731 322404 10898.34 8166.591 55.18222 1016 [5,] 333594 28915 322404 10991.73 8215.355 55.18222 1016 [6,] 333594 29099 322404 11067.63 8254.604 55.18222 1016 $forecasts$ets YAF2 YAF3 YAF4 YAF5 YAF6 YAF7 YAF8 YAF9 [1,] 556280.7 384603.9 381979.7 318277.4 21230649 16129.36 847700.2 638290.3 [2,] 594333.0 385162.7 399547.7 334201.6 21690238 17323.96 847700.2 638290.3 [3,] 632385.3 385721.5 417115.8 350125.8 22149828 18518.57 847700.2 638290.3 [4,] 670437.6 386280.4 434683.8 366050.0 22609417 19713.17 847700.2 638290.3 [5,] 708489.9 386839.2 452251.8 381974.2 23069007 20907.77 847700.2 638290.3 [6,] 746542.3 387398.0 469819.8 397898.4 23528597 22102.37 847700.2 638290.3 YAF10 YAF11 YAF12 YAF13 YAF14 YAF15 YAF16 YAF17 [1,] 862123.4 55.61797 9062.936 1891552 50919.17 863495.4 1041.897 8.758337 [2,] 862123.4 57.30610 9694.528 2071283 51415.28 852236.8 1041.897 8.933332 [3,] 862123.4 58.99423 10326.120 2251013 51911.39 840978.2 1041.897 9.108327 [4,] 862123.4 60.68236 10957.713 2430744 52407.51 829719.7 1041.897 9.283322 [5,] 862123.4 62.37049 11589.305 2610474 52903.62 818461.1 1041.897 9.458317 [6,] 862123.4 64.05862 12220.897 2790205 53399.73 807202.5 1041.897 9.633312 YAM1 YAM2 YAM3 YAM4 YAM5 YAM6 YAM7 YAM8 [1,] 71904.8 622496.4 7288.029 18139.21 26.90008 2.751001 1768.626 94.19305 [2,] 71904.8 643385.2 7473.800 18139.21 26.90008 2.763292 1616.066 94.19305 [3,] 71904.8 664274.1 7655.277 18139.21 26.90008 2.775582 1463.505 94.19305 [4,] 71904.8 685163.0 7832.559 18139.21 26.90008 2.787872 1310.945 94.19305 [5,] 71904.8 706051.8 8005.744 18139.21 26.90008 2.800163 1158.384 94.19305 [6,] 71904.8 726940.7 8174.927 18139.21 26.90008 2.812453 1005.824 94.19305 YAM10 YAM11 YAM12 YAM13 YAM14 YAM15 YAM16 YAM17 [1,] 51.40864 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698 [2,] 45.01771 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698 [3,] 38.62677 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698 [4,] 32.23584 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698 [5,] 25.84490 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698 [6,] 19.45397 20541561 13117340 3114.108 811.0047 771.36 95.40857 195.4698 YAM18 YAM19 YAM20 YAM21 YAM22 YAM23 YAM24 YAM25 [1,] 5772.765 98.45844 9383.001 192.915 102.7997 12572.73 9445.22 11882.67 [2,] 5963.491 98.45844 9383.001 192.915 102.7997 13092.52 9840.36 12139.31 [3,] 6154.217 98.45844 9383.001 192.915 102.7997 13612.32 10235.50 12395.95 [4,] 6344.944 98.45844 9383.001 192.915 102.7997 14132.12 10630.64 12652.59 [5,] 6535.670 98.45844 9383.001 192.915 102.7997 14651.91 11025.78 12909.23 [6,] 6726.397 98.45844 9383.001 192.915 102.7997 15171.71 11420.92 13165.87 YAM26 YAM27 YAM28 YAM29 YAM30 YAB1 YAB2 YAB3 [1,] 25408.03 598.1309 1294.571 8034.943 67724.98 29808.78 7413.43 632495.6 [2,] 25408.03 648.6591 1399.941 8034.943 68437.20 29808.78 7413.43 689561.2 [3,] 25408.03 699.1873 1505.311 8034.943 69149.43 29808.78 7413.43 746626.8 [4,] 25408.03 749.7155 1610.681 8034.943 69861.65 29808.78 7413.43 803692.4 [5,] 25408.03 800.2437 1716.051 8034.943 70573.87 29808.78 7413.43 860758.0 [6,] 25408.03 850.7720 1821.420 8034.943 71286.09 29808.78 7413.43 917823.6 YAB4 YAB5 YAB6 YAB7 YAB8 YAB9 YAB10 YAB11 [1,] 77761.55 10640.79 765.3444 717627.4 170008.5 249081.6 39097.8 142154.7 [2,] 77761.55 11009.85 787.3006 743153.2 170008.5 268377.3 39097.8 142154.7 [3,] 77761.55 11378.91 809.2567 768679.0 170008.5 287673.0 39097.8 142154.7 [4,] 77761.55 11747.97 831.2129 794204.8 170008.5 306968.7 39097.8 142154.7 [5,] 77761.55 12117.03 853.1691 819730.6 170008.5 326264.5 39097.8 142154.7 [6,] 77761.55 12486.09 875.1253 845256.4 170008.5 345560.2 39097.8 142154.7 YAB12 YAI1 YAI2 YAI3 YAI4 YAI5 YAI6 YAI7 [1,] 26693.34 1230.370 39176.12 223.3444 2935.279 756.0147 1944587 21800234 [2,] 26827.99 1274.384 39176.12 223.3444 2935.279 756.0147 2035542 21800234 [3,] 26962.64 1318.399 39176.12 223.3444 2935.279 756.0147 2126498 21800234 [4,] 27097.28 1362.414 39176.12 223.3444 2935.279 756.0147 2217453 21800234 [5,] 27231.93 1406.428 39176.12 223.3444 2935.279 756.0147 2308408 21800234 [6,] 27366.58 1450.443 39176.12 223.3444 2935.279 756.0147 2399363 21800234 YAI8 YAI9 YAI10 YAI11 YAI12 YAI13 YAI14 YAI15 [1,] 8585.218 279.6960 219148.7 627.7966 1575.805 1294.276 810.0796 246.3978 [2,] 8585.218 299.0945 226157.3 627.7966 1679.404 1550.172 810.0796 259.6593 [3,] 8585.218 318.4930 233165.9 627.7966 1783.002 1806.068 810.0796 272.9209 [4,] 8585.218 337.8915 240174.5 627.7966 1886.601 2061.965 810.0796 286.1824 [5,] 8585.218 357.2900 247183.1 627.7966 1990.200 2317.861 810.0796 299.4439 [6,] 8585.218 376.6884 254191.8 627.7966 2093.798 2573.757 810.0796 312.7054 YAI16 YAI17 YAI18 YAI19 YAI20 YAI21 YAI22 YAI23 [1,] 150.4702 1272.175 114.9165 38.20008 14.05925 1294.571 3116.417 23.35369 [2,] 161.7391 1272.175 114.9165 38.20008 14.05925 1399.941 3116.417 23.35369 [3,] 173.0080 1272.175 114.9165 38.20008 14.05925 1505.311 3116.417 23.35369 [4,] 184.2770 1272.175 114.9165 38.20008 14.05925 1610.681 3116.417 23.35369 [5,] 195.5459 1272.175 114.9165 38.20008 14.05925 1716.051 3116.417 23.35369 [6,] 206.8149 1272.175 114.9165 38.20008 14.05925 1821.420 3116.417 23.35369 YAI24 YAI25 YAI26 YAI27 YAI28 YAI29 YAI30 YAI31 [1,] 144346.9 60.66101 682.1895 4366.951 387.0890 151.2821 16.75260 6.380076 [2,] 153609.4 64.52041 697.7193 4809.599 402.4771 157.9637 17.76071 6.380076 [3,] 162872.0 68.37980 713.2492 5252.247 417.8652 164.6454 18.76882 6.380076 [4,] 172134.5 72.23920 728.7790 5694.895 433.2533 171.3271 19.77693 6.380076 [5,] 181397.1 76.09860 744.3089 6137.543 448.6414 178.0087 20.78504 6.380076 [6,] 190659.6 79.95799 759.8388 6580.191 464.0295 184.6904 21.79315 6.380076 YAI32 YAI33 YAI34 YAI35 YAG1 YAG2 YAG3 YAG4 [1,] 14.2 7.863819 3.334205 2.799162 236.2488 52.51979 92.29229 10.83798 [2,] 14.2 7.863819 3.334205 2.799162 243.8410 52.51979 99.96504 10.83798 [3,] 14.2 7.863819 3.334205 2.799162 251.4332 52.51979 107.63780 10.83798 [4,] 14.2 7.863819 3.334205 2.799162 259.0254 52.51979 115.31055 10.83798 [5,] 14.2 7.863819 3.334205 2.799162 266.6176 52.51979 122.98330 10.83798 [6,] 14.2 7.863819 3.334205 2.799162 274.2099 52.51979 130.65605 10.83798 YAG5 YAG6 YAG7 YAG8 YAG9 YAG10 YAG11 YAG12 [1,] 119.9995 105.3229 112.8678 187.9984 125.9992 92.39959 366156.5 107237.2 [2,] 124.9992 105.3229 112.8678 187.9984 125.9992 92.39959 379417.3 107237.2 [3,] 129.9988 105.3229 112.8678 187.9984 125.9992 92.39959 392678.1 107237.2 [4,] 134.9985 105.3229 112.8678 187.9984 125.9992 92.39959 405938.8 107237.2 [5,] 139.9981 105.3229 112.8678 187.9984 125.9992 92.39959 419199.6 107237.2 [6,] 144.9978 105.3229 112.8678 187.9984 125.9992 92.39959 432460.4 107237.2 YAG13 YAG14 YAG15 YAG16 YAG17 YAG18 YAG19 YAG20 [1,] 96645.48 4317.518 30435.68 471558.6 41.41975 597.9932 616.1694 877.4688 [2,] 100051.24 4317.518 31600.27 488490.1 41.41975 597.9932 663.3367 896.8383 [3,] 103457.00 4317.518 32764.86 505421.5 41.41975 597.9932 710.5040 916.2079 [4,] 106862.75 4317.518 33929.45 522353.0 41.41975 597.9932 757.6713 935.5774 [5,] 110268.51 4317.518 35094.03 539284.5 41.41975 597.9932 804.8386 954.9469 [6,] 113674.27 4317.518 36258.62 556215.9 41.41975 597.9932 852.0059 974.3164 YAG21 YAG22 YAG23 YAG24 YAG25 YAG26 YAG27 YAG28 [1,] 5.676057 10.28459 137.1325 65.55742 22.06471 11.73084 6.194973 7.658353 [2,] 5.861596 10.66136 142.7652 67.58464 22.76828 12.24912 6.545724 7.920919 [3,] 6.047134 11.03812 148.3979 69.61186 23.47184 12.76740 6.896474 8.183485 [4,] 6.232673 11.41489 154.0306 71.63908 24.17541 13.28567 7.247224 8.446052 [5,] 6.418211 11.79165 159.6634 73.66630 24.87898 13.80395 7.597974 8.708618 [6,] 6.603750 12.16842 165.2961 75.69353 25.58254 14.32223 7.948724 8.971185 YAG29 YAG30 YAC1 YAC2 YAC3 YAC4 YAC5 YAC6 [1,] 8.055765 4.436833 75.11300 27.10459 18.73374 23.77300 95.77583 19.50443 [2,] 8.411540 4.673677 77.04760 27.98003 19.72020 26.30834 98.62324 19.50443 [3,] 8.767315 4.910521 78.98220 28.85547 20.70665 28.84368 101.47066 19.50443 [4,] 9.123091 5.147365 80.91680 29.73091 21.69311 31.37902 104.31808 19.50443 [5,] 9.478866 5.384209 82.85141 30.60635 22.67957 33.91435 107.16550 19.50443 [6,] 9.834641 5.621053 84.78601 31.48179 23.66602 36.44969 110.01291 19.50443 YAC7 YAC8 YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 [1,] 32.33359 28.28980 42.73003 73781.77 32065.89 53562.68 39957.31 52763.99 [2,] 33.03120 30.90142 46.52828 73781.77 32844.40 56028.30 41191.43 52763.99 [3,] 33.72881 33.51303 50.32652 73781.77 33622.91 58493.91 42425.55 52763.99 [4,] 34.42642 36.12465 54.12477 73781.77 34401.42 60959.53 43659.67 52763.99 [5,] 35.12403 38.73626 57.92302 73781.77 35179.92 63425.14 44893.79 52763.99 [6,] 35.82165 41.34788 61.72126 73781.77 35958.43 65890.76 46127.90 52763.99 YAC15 YAC16 YAC17 YAC18 YAC19 YAC20 YAC21 YAC22 [1,] 58574.27 25962.29 32594.29 54.59722 31385663 5325.901 2082.296 2091.260 [2,] 62860.50 25962.29 33675.17 56.69452 31385663 5539.986 2152.363 2239.474 [3,] 67146.73 25962.29 34756.04 58.79181 31385663 5754.071 2222.431 2387.689 [4,] 71432.96 25962.29 35836.92 60.88911 31385663 5968.156 2292.499 2535.903 [5,] 75719.19 25962.29 36917.80 62.98641 31385663 6182.241 2362.566 2684.118 [6,] 80005.42 25962.29 37998.67 65.08370 31385663 6396.326 2432.634 2832.332 YAC23 YAC24 YAC25 YAC26 YAC27 YAC28 YAC29 YAD1 [1,] 1797.065 1803.988 3382.958 890.9938 1686.843 2395.335 2045.002 114.6321 [2,] 1892.605 1803.988 3600.915 890.9938 1824.681 2499.652 2045.002 114.6321 [3,] 1988.145 1803.988 3818.872 890.9938 1962.520 2603.968 2045.002 114.6321 [4,] 2083.684 1803.988 4036.828 890.9938 2100.358 2708.285 2045.002 114.6321 [5,] 2179.224 1803.988 4254.785 890.9938 2238.196 2812.602 2045.002 114.6321 [6,] 2274.764 1803.988 4472.742 890.9938 2376.035 2916.918 2045.002 114.6321 YAD2 YAD3 YAD4 YAD5 YAD6 YAD7 YAD8 YAD9 [1,] 36599.87 290.6517 1917.219 491.9706 448.7009 438.1286 886.3374 888.2836 [2,] 36697.57 291.1678 1917.219 491.9706 448.7009 439.4655 889.4333 888.2836 [3,] 36793.12 291.6615 1917.219 491.9706 448.7009 440.8024 892.5292 888.2836 [4,] 36886.59 292.1336 1917.219 491.9706 448.7009 442.1393 895.6251 888.2836 [5,] 36978.01 292.5853 1917.219 491.9706 448.7009 443.4762 898.7209 888.2836 [6,] 37067.42 293.0172 1917.219 491.9706 448.7009 444.8132 901.8168 888.2836 YAD10 YAD11 YAD12 YAD13 YAD14 YAD15 YAD16 YAD17 [1,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6 [2,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6 [3,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6 [4,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6 [5,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6 [6,] 959.2861 3597.253 37.1223 40.0969 1005.923 23.20005 9.411108 411630.6 YAD18 YAD19 YAD20 YAD21 YAD22 YAD23 YAD24 YAD25 [1,] 2.334264 1551118 638.9945 26631.33 469.7187 442.9032 326656.7 28178.30 [2,] 2.334264 1551118 638.9945 26820.24 469.7187 442.9032 326656.7 28362.21 [3,] 2.334264 1551118 638.9945 27009.14 469.7187 442.9032 326656.7 28546.12 [4,] 2.334264 1551118 638.9945 27198.05 469.7187 442.9032 326656.7 28730.02 [5,] 2.334264 1551118 638.9945 27386.95 469.7187 442.9032 326656.7 28913.93 [6,] 2.334264 1551118 638.9945 27575.86 469.7187 442.9032 326656.7 29097.83 YAD26 YAD27 YAD28 YAD29 YAD30 [1,] 313613.9 10254.09 7821.031 56.20631 1016.286 [2,] 313613.9 10254.09 7821.031 56.20631 1016.286 [3,] 313613.9 10254.09 7821.031 56.20631 1016.286 [4,] 313613.9 10254.09 7821.031 56.20631 1016.286 [5,] 313613.9 10254.09 7821.031 56.20631 1016.286 [6,] 313613.9 10254.09 7821.031 56.20631 1016.286 $forecasts$rw YAF2 YAF3 YAF4 YAF5 YAF6 YAF7 YAF8 YAF9 YAF10 YAF11 [1,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93 [2,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93 [3,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93 [4,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93 [5,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93 [6,] 553400 384040 362207 350083 18752400 14979.9 847706 638296 862129 53.93 YAF12 YAF13 YAF14 YAF15 YAF16 YAF17 YAM1 YAM2 YAM3 YAM4 YAM5 [1,] 8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9 [2,] 8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9 [3,] 8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9 [4,] 8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9 [5,] 8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9 [6,] 8447 1711840 50423 866498 1041.9 8.58397 71755 666224 6856.47 18139 26.9 YAM6 YAM7 YAM8 YAM10 YAM11 YAM12 YAM13 YAM14 YAM15 YAM16 YAM17 [1,] 2.74031 1919.4 71.6 57.8 20525000 13056000 3482 811 770 100.8 175 [2,] 2.74031 1919.4 71.6 57.8 20525000 13056000 3482 811 770 100.8 175 [3,] 2.74031 1919.4 71.6 57.8 20525000 13056000 3482 811 770 100.8 175 [4,] 2.74031 1919.4 71.6 57.8 20525000 13056000 3482 811 770 100.8 175 [5,] 2.74031 1919.4 71.6 57.8 20525000 13056000 3482 811 770 100.8 175 [6,] 2.74031 1919.4 71.6 57.8 20525000 13056000 3482 811 770 100.8 175 YAM18 YAM19 YAM20 YAM21 YAM22 YAM23 YAM24 YAM25 YAM26 YAM27 YAM28 YAM29 [1,] 5582 101.4 9383 207.95 102.8 12053 9050 11626 25408 559 1219 8035 [2,] 5582 101.4 9383 207.95 102.8 12053 9050 11626 25408 559 1219 8035 [3,] 5582 101.4 9383 207.95 102.8 12053 9050 11626 25408 559 1219 8035 [4,] 5582 101.4 9383 207.95 102.8 12053 9050 11626 25408 559 1219 8035 [5,] 5582 101.4 9383 207.95 102.8 12053 9050 11626 25408 559 1219 8035 [6,] 5582 101.4 9383 207.95 102.8 12053 9050 11626 25408 559 1219 8035 YAM30 YAB1 YAB2 YAB3 YAB4 YAB5 YAB6 YAB7 YAB8 YAB9 YAB10 YAB11 [1,] 74667 29809 7555 588478 80389 10185 660 692102 147233 229789 39098 142157 [2,] 74667 29809 7555 588478 80389 10185 660 692102 147233 229789 39098 142157 [3,] 74667 29809 7555 588478 80389 10185 660 692102 147233 229789 39098 142157 [4,] 74667 29809 7555 588478 80389 10185 660 692102 147233 229789 39098 142157 [5,] 74667 29809 7555 588478 80389 10185 660 692102 147233 229789 39098 142157 [6,] 74667 29809 7555 588478 80389 10185 660 692102 147233 229789 39098 142157 YAB12 YAI1 YAI2 YAI3 YAI4 YAI5 YAI6 YAI7 YAI8 YAI9 YAI10 YAI11 [1,] 26869 1191 39177 365 2977 756 1859860 21800200 8800.8 270 212140 632.6 [2,] 26869 1191 39177 365 2977 756 1859860 21800200 8800.8 270 212140 632.6 [3,] 26869 1191 39177 365 2977 756 1859860 21800200 8800.8 270 212140 632.6 [4,] 26869 1191 39177 365 2977 756 1859860 21800200 8800.8 270 212140 632.6 [5,] 26869 1191 39177 365 2977 756 1859860 21800200 8800.8 270 212140 632.6 [6,] 26869 1191 39177 365 2977 756 1859860 21800200 8800.8 270 212140 632.6 YAI12 YAI13 YAI14 YAI15 YAI16 YAI17 YAI18 YAI19 YAI20 YAI21 YAI22 [1,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5 38.2 13.936 1219 3116.4 [2,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5 38.2 13.936 1219 3116.4 [3,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5 38.2 13.936 1219 3116.4 [4,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5 38.2 13.936 1219 3116.4 [5,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5 38.2 13.936 1219 3116.4 [6,] 1472.2 1038.4 810.1 247.1 139.2 1272.2 111.5 38.2 13.936 1219 3116.4 YAI23 YAI24 YAI25 YAI26 YAI27 YAI28 YAI29 YAI30 YAI31 YAI32 YAI33 YAI34 [1,] 24 131194 56.8 470 3840 371.7 144.6 16.34 6.38 14.2 9.33 3.34 [2,] 24 131194 56.8 470 3840 371.7 144.6 16.34 6.38 14.2 9.33 3.34 [3,] 24 131194 56.8 470 3840 371.7 144.6 16.34 6.38 14.2 9.33 3.34 [4,] 24 131194 56.8 470 3840 371.7 144.6 16.34 6.38 14.2 9.33 3.34 [5,] 24 131194 56.8 470 3840 371.7 144.6 16.34 6.38 14.2 9.33 3.34 [6,] 24 131194 56.8 470 3840 371.7 144.6 16.34 6.38 14.2 9.33 3.34 YAI35 YAG1 YAG2 YAG3 YAG4 YAG5 YAG6 YAG7 YAG8 YAG9 YAG10 YAG11 [1,] 2.84 237.6 52.52 84.66 11.39 115 107.69 117 188 126 92.4 356556 [2,] 2.84 237.6 52.52 84.66 11.39 115 107.69 117 188 126 92.4 356556 [3,] 2.84 237.6 52.52 84.66 11.39 115 107.69 117 188 126 92.4 356556 [4,] 2.84 237.6 52.52 84.66 11.39 115 107.69 117 188 126 92.4 356556 [5,] 2.84 237.6 52.52 84.66 11.39 115 107.69 117 188 126 92.4 356556 [6,] 2.84 237.6 52.52 84.66 11.39 115 107.69 117 188 126 92.4 356556 YAG12 YAG13 YAG14 YAG15 YAG16 YAG17 YAG18 YAG19 YAG20 YAG21 YAG22 YAG23 [1,] 107238 93951 6347 30278 460613 41.42 598 569 858.1 5.6 10.1 131.5 [2,] 107238 93951 6347 30278 460613 41.42 598 569 858.1 5.6 10.1 131.5 [3,] 107238 93951 6347 30278 460613 41.42 598 569 858.1 5.6 10.1 131.5 [4,] 107238 93951 6347 30278 460613 41.42 598 569 858.1 5.6 10.1 131.5 [5,] 107238 93951 6347 30278 460613 41.42 598 569 858.1 5.6 10.1 131.5 [6,] 107238 93951 6347 30278 460613 41.42 598 569 858.1 5.6 10.1 131.5 YAG24 YAG25 YAG26 YAG27 YAG28 YAG29 YAG30 YAC1 YAC2 YAC3 YAC4 YAC5 [1,] 63.1 22.1 11.3 6 7.4 7.7 4.2 74.51 27.65 17.7 22.09 95.65 [2,] 63.1 22.1 11.3 6 7.4 7.7 4.2 74.51 27.65 17.7 22.09 95.65 [3,] 63.1 22.1 11.3 6 7.4 7.7 4.2 74.51 27.65 17.7 22.09 95.65 [4,] 63.1 22.1 11.3 6 7.4 7.7 4.2 74.51 27.65 17.7 22.09 95.65 [5,] 63.1 22.1 11.3 6 7.4 7.7 4.2 74.51 27.65 17.7 22.09 95.65 [6,] 63.1 22.1 11.3 6 7.4 7.7 4.2 74.51 27.65 17.7 22.09 95.65 YAC6 YAC7 YAC8 YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 YAC15 YAC16 YAC17 [1,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460 [2,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460 [3,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460 [4,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460 [5,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460 [6,] 19.84 32.69 25.63 38.93 73782 31860 51835 40034 52950 54288 26875 32460 YAC18 YAC19 YAC20 YAC21 YAC22 YAC23 YAC24 YAC25 YAC26 YAC27 YAC28 YAC29 [1,] 52.5 31441200 5141 2017 1955 1654 1804 3165 891 1549 2291 2045 [2,] 52.5 31441200 5141 2017 1955 1654 1804 3165 891 1549 2291 2045 [3,] 52.5 31441200 5141 2017 1955 1654 1804 3165 891 1549 2291 2045 [4,] 52.5 31441200 5141 2017 1955 1654 1804 3165 891 1549 2291 2045 [5,] 52.5 31441200 5141 2017 1955 1654 1804 3165 891 1549 2291 2045 [6,] 52.5 31441200 5141 2017 1955 1654 1804 3165 891 1549 2291 2045 YAD1 YAD2 YAD3 YAD4 YAD5 YAD6 YAD7 YAD8 YAD9 YAD10 YAD11 YAD12 YAD13 [1,] 142 36500 298 1546 522 492 487 979 937 1018 4088 37.1 39.8 [2,] 142 36500 298 1546 522 492 487 979 937 1018 4088 37.1 39.8 [3,] 142 36500 298 1546 522 492 487 979 937 1018 4088 37.1 39.8 [4,] 142 36500 298 1546 522 492 487 979 937 1018 4088 37.1 39.8 [5,] 142 36500 298 1546 522 492 487 979 937 1018 4088 37.1 39.8 [6,] 142 36500 298 1546 522 492 487 979 937 1018 4088 37.1 39.8 YAD14 YAD15 YAD16 YAD17 YAD18 YAD19 YAD20 YAD21 YAD22 YAD23 YAD24 [1,] 963 23.2 9.3 413000 2.35 1577360 639 26441 473 446 333594 [2,] 963 23.2 9.3 413000 2.35 1577360 639 26441 473 446 333594 [3,] 963 23.2 9.3 413000 2.35 1577360 639 26441 473 446 333594 [4,] 963 23.2 9.3 413000 2.35 1577360 639 26441 473 446 333594 [5,] 963 23.2 9.3 413000 2.35 1577360 639 26441 473 446 333594 [6,] 963 23.2 9.3 413000 2.35 1577360 639 26441 473 446 333594 YAD25 YAD26 YAD27 YAD28 YAD29 YAD30 [1,] 27995 322404 10254 7821 56.49 1016 [2,] 27995 322404 10254 7821 56.49 1016 [3,] 27995 322404 10254 7821 56.49 1016 [4,] 27995 322404 10254 7821 56.49 1016 [5,] 27995 322404 10254 7821 56.49 1016 [6,] 27995 322404 10254 7821 56.49 1016 $forecasts$rwd YAF2 YAF3 YAF4 YAF5 YAF6 YAF7 YAF8 YAF9 [1,] 579581.0 400921.2 378573.6 365733.4 19234508 15566.79 904964.3 673803.7 [2,] 605761.9 417802.4 394940.2 381383.8 19716615 16153.68 962222.7 709311.4 [3,] 631942.9 434683.5 411306.8 397034.2 20198723 16740.58 1019481.0 744819.1 [4,] 658123.8 451564.7 427673.4 412684.6 20680830 17327.47 1076739.3 780326.8 [5,] 684304.8 468445.9 444040.0 428335.0 21162938 17914.36 1133997.7 815834.5 [6,] 710485.7 485327.1 460406.5 443985.5 21645045 18501.25 1191256.0 851342.2 YAF10 YAF11 YAF12 YAF13 YAF14 YAF15 YAF16 YAF17 [1,] 906621.4 55.13 8765.6 1775160 51406.53 908663.9 1084.355 8.764490 [2,] 951113.8 56.33 9084.2 1838480 52390.06 950829.8 1126.809 8.945009 [3,] 995606.1 57.53 9402.8 1901800 53373.59 992995.7 1169.264 9.125529 [4,] 1040098.5 58.73 9721.4 1965120 54357.12 1035161.6 1211.718 9.306048 [5,] 1084590.9 59.93 10040.0 2028441 55340.65 1077327.5 1254.173 9.486568 [6,] 1129083.2 61.13 10358.6 2091761 56324.18 1119493.4 1296.627 9.667087 YAM1 YAM2 YAM3 YAM4 YAM5 YAM6 YAM7 YAM8 [1,] 74969.09 697948.7 7089.829 18996.05 24.85833 2.753552 2031.144 76.60833 [2,] 78183.18 729673.4 7323.188 19853.10 22.81667 2.766793 2142.888 81.61667 [3,] 81397.27 761398.1 7556.547 20710.14 20.77500 2.780035 2254.631 86.62500 [4,] 84611.36 793122.9 7789.906 21567.19 18.73333 2.793276 2366.375 91.63333 [5,] 87825.45 824847.6 8023.265 22424.24 16.69167 2.806518 2478.119 96.64167 [6,] 91039.55 856572.3 8256.624 23281.29 14.65000 2.819759 2589.863 101.65000 YAM10 YAM11 YAM12 YAM13 YAM14 YAM15 YAM16 YAM17 [1,] 60.54762 20667008 13014517 3527.625 822.6842 780.3333 101.9238 179.9231 [2,] 63.29524 20809017 12973033 3573.250 834.3684 790.6667 103.0476 184.8462 [3,] 66.04286 20951025 12931550 3618.875 846.0526 801.0000 104.1714 189.7692 [4,] 68.79048 21093033 12890067 3664.500 857.7368 811.3333 105.2952 194.6923 [5,] 71.53810 21235042 12848583 3710.125 869.4211 821.6667 106.4190 199.6154 [6,] 74.28571 21377050 12807100 3755.750 881.1053 832.0000 107.5429 204.5385 YAM18 YAM19 YAM20 YAM21 YAM22 YAM23 YAM24 YAM25 [1,] 5773.286 102.6857 9394.15 209.1556 105.1143 12469.10 9352.15 11898.3 [2,] 5964.571 103.9714 9405.30 210.3611 107.4286 12885.19 9654.30 12170.6 [3,] 6155.857 105.2571 9416.45 211.5667 109.7429 13301.29 9956.45 12442.9 [4,] 6347.143 106.5429 9427.60 212.7722 112.0571 13717.38 10258.60 12715.2 [5,] 6538.429 107.8286 9438.75 213.9778 114.3714 14133.48 10560.75 12987.5 [6,] 6729.714 109.1143 9449.90 215.1833 116.6857 14549.57 10862.90 13259.8 YAM26 YAM27 YAM28 YAM29 YAM30 YAB1 YAB2 YAB3 [1,] 25885.5 584.95 1267.55 8074.688 76266.65 31148.35 7913.095 621170.9 [2,] 26363.0 610.90 1316.10 8114.375 77866.30 32487.70 8271.190 653863.9 [3,] 26840.5 636.85 1364.65 8154.062 79465.96 33827.05 8629.286 686556.8 [4,] 27318.0 662.80 1413.20 8193.750 81065.61 35166.40 8987.381 719249.8 [5,] 27795.5 688.75 1461.75 8233.438 82665.26 36505.75 9345.476 751942.7 [6,] 28273.0 714.70 1510.30 8273.125 84264.91 37845.10 9703.571 784635.7 YAB4 YAB5 YAB6 YAB7 YAB8 YAB9 YAB10 YAB11 [1,] 84186.67 10547.31 672.5814 718453.1 148108.9 250283.4 41750.27 147471.1 [2,] 87984.33 10909.62 685.1628 744804.2 148984.8 270777.7 44402.55 152785.2 [3,] 91782.00 11271.94 697.7442 771155.3 149860.7 291272.1 47054.82 158099.3 [4,] 95579.67 11634.25 710.3256 797506.4 150736.6 311766.5 49707.09 163413.4 [5,] 99377.33 11996.56 722.9070 823857.5 151612.5 332260.8 52359.36 168727.5 [6,] 103175.00 12358.88 735.4884 850208.5 152488.5 352755.2 55011.64 174041.5 YAB12 YAI1 YAI2 YAI3 YAI4 YAI5 YAI6 YAI7 [1,] 27054.21 1257.088 40285.68 371.7368 3014.289 759.9211 1910418 22286105 [2,] 27239.42 1323.176 41394.36 378.4737 3051.579 763.8421 1960976 22772011 [3,] 27424.63 1389.265 42503.04 385.2105 3088.868 767.7632 2011534 23257916 [4,] 27609.84 1455.353 43611.72 391.9474 3126.158 771.6842 2062092 23743822 [5,] 27795.05 1521.441 44720.40 398.6842 3163.447 775.6053 2112651 24229727 [6,] 27980.26 1587.529 45829.08 405.4211 3200.737 779.5263 2163209 24715632 YAI8 YAI9 YAI10 YAI11 YAI12 YAI13 YAI14 YAI15 [1,] 9174.941 290.2 217400 662.7529 1558.371 1098.188 870.4231 260.4941 [2,] 9549.082 310.4 222660 692.9059 1644.541 1157.976 930.7462 273.8882 [3,] 9923.224 330.6 227920 723.0588 1730.712 1217.765 991.0692 287.2824 [4,] 10297.365 350.8 233180 753.2118 1816.882 1277.553 1051.3923 300.6765 [5,] 10671.506 371.0 238440 783.3647 1903.053 1337.341 1111.7154 314.0706 [6,] 11045.647 391.2 243700 813.5176 1989.224 1397.129 1172.0385 327.4647 YAI16 YAI17 YAI18 YAI19 YAI20 YAI21 YAI22 YAI23 [1,] 146.8882 1332.518 108.93833 39.08333 13.74358 1267.55 3205.167 24.22632 [2,] 154.5765 1392.835 106.37667 39.96667 13.55117 1316.10 3293.935 24.45263 [3,] 162.2647 1453.153 103.81500 40.85000 13.35875 1364.65 3382.702 24.67895 [4,] 169.9529 1513.471 101.25333 41.73333 13.16633 1413.20 3471.470 24.90526 [5,] 177.6412 1573.788 98.69167 42.61667 12.97392 1461.75 3560.237 25.13158 [6,] 185.3294 1634.106 96.13000 43.50000 12.78150 1510.30 3649.005 25.35789 YAI24 YAI25 YAI26 YAI27 YAI28 YAI29 YAI30 YAI31 [1,] 135512 59.07368 472.9444 4044.167 388.0684 150.4105 17.555 6.552727 [2,] 139830 61.34737 475.8889 4248.333 404.4368 156.2211 18.770 6.725455 [3,] 144148 63.62105 478.8333 4452.500 420.8053 162.0316 19.985 6.898182 [4,] 148466 65.89474 481.7778 4656.667 437.1737 167.8421 21.200 7.070909 [5,] 152784 68.16842 484.7222 4860.833 453.5421 173.6526 22.415 7.243636 [6,] 157102 70.44211 487.6667 5065.000 469.9105 179.4632 23.630 7.416364 YAI32 YAI33 YAI34 YAI35 YAG1 YAG2 YAG3 YAG4 [1,] 14.43333 9.511667 3.46 2.850909 245.9575 53.90333 88.745 11.84167 [2,] 14.66667 9.693333 3.58 2.861818 254.3150 55.28667 92.830 12.29333 [3,] 14.90000 9.875000 3.70 2.872727 262.6725 56.67000 96.915 12.74500 [4,] 15.13333 10.056667 3.82 2.883636 271.0300 58.05333 101.000 13.19667 [5,] 15.36667 10.238333 3.94 2.894545 279.3875 59.43667 105.085 13.64833 [6,] 15.60000 10.420000 4.06 2.905455 287.7450 60.82000 109.170 14.10000 YAG5 YAG6 YAG7 YAG8 YAG9 YAG10 YAG11 YAG12 [1,] 118.8125 113.3922 117.5833 191.3611 127.2121 95.52632 370305.5 113285.7 [2,] 122.6250 119.0944 118.1667 194.7222 128.4242 98.65263 384055.0 119333.3 [3,] 126.4375 124.7967 118.7500 198.0833 129.6364 101.77895 397804.5 125381.0 [4,] 130.2500 130.4989 119.3333 201.4444 130.8485 104.90526 411554.0 131428.7 [5,] 134.0625 136.2011 119.9167 204.8056 132.0606 108.03158 425303.5 137476.3 [6,] 137.8750 141.9033 120.5000 208.1667 133.2727 111.15789 439053.0 143524.0 YAG13 YAG14 YAG15 YAG16 YAG17 YAG18 YAG19 YAG20 [1,] 97293.5 6330.5 31650.58 478816.8 42.49533 630.8182 599.6364 868.4811 [2,] 100636.0 6314.0 33023.17 497020.7 43.57067 663.6364 630.2727 878.8622 [3,] 103978.5 6297.5 34395.75 515224.5 44.64600 696.4545 660.9091 889.2432 [4,] 107321.0 6281.0 35768.33 533428.3 45.72133 729.2727 691.5455 899.6243 [5,] 110663.5 6264.5 37140.92 551632.2 46.79667 762.0909 722.1818 910.0054 [6,] 114006.0 6248.0 38513.50 569836.0 47.87200 794.9091 752.8182 920.3865 YAG21 YAG22 YAG23 YAG24 YAG25 YAG26 YAG27 YAG28 [1,] 5.807143 10.48571 137.5071 65.54286 22.85714 11.62857 6.25 7.664286 [2,] 6.014286 10.87143 143.5143 67.98571 23.61429 11.95714 6.50 7.928571 [3,] 6.221429 11.25714 149.5214 70.42857 24.37143 12.28571 6.75 8.192857 [4,] 6.428571 11.64286 155.5286 72.87143 25.12857 12.61429 7.00 8.457143 [5,] 6.635714 12.02857 161.5357 75.31429 25.88571 12.94286 7.25 8.721429 [6,] 6.842857 12.41429 167.5429 77.75714 26.64286 13.27143 7.50 8.985714 YAG29 YAG30 YAC1 YAC2 YAC3 YAC4 YAC5 YAC6 YAC7 [1,] 7.935714 4.342857 76.5825 28.6575 18.36 23.45917 98.85917 20.28667 33.625 [2,] 8.171429 4.485714 78.6550 29.6650 19.02 24.82833 102.06833 20.73333 34.560 [3,] 8.407143 4.628571 80.7275 30.6725 19.68 26.19750 105.27750 21.18000 35.495 [4,] 8.642857 4.771429 82.8000 31.6800 20.34 27.56667 108.48667 21.62667 36.430 [5,] 8.878571 4.914286 84.8725 32.6875 21.00 28.93583 111.69583 22.07333 37.365 [6,] 9.114286 5.057143 86.9450 33.6950 21.66 30.30500 114.90500 22.52000 38.300 YAC8 YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 YAC15 [1,] 26.5675 40.89083 75474.42 32767.92 54381.67 41238.08 56175.58 57110.08 [2,] 27.5050 42.85167 77166.83 33675.83 56928.33 42442.17 59401.17 59932.17 [3,] 28.4425 44.81250 78859.25 34583.75 59475.00 43646.25 62626.75 62754.25 [4,] 29.3800 46.77333 80551.67 35491.67 62021.67 44850.33 65852.33 65576.33 [5,] 30.3175 48.73417 82244.08 36399.58 64568.33 46054.42 69077.92 68398.42 [6,] 31.2550 50.69500 83936.50 37307.50 67115.00 47258.50 72303.50 71220.50 YAC16 YAC17 YAC18 YAC19 YAC20 YAC21 YAC22 YAC23 YAC24 [1,] 27463.75 33610.5 54.46667 32175926 5350.167 2083.917 2047.833 1743 1886.5 [2,] 28052.50 34761.0 56.43333 32910651 5559.333 2150.833 2140.667 1832 1969.0 [3,] 28641.25 35911.5 58.40000 33645377 5768.500 2217.750 2233.500 1921 2051.5 [4,] 29230.00 37062.0 60.36667 34380102 5977.667 2284.667 2326.333 2010 2134.0 [5,] 29818.75 38212.5 62.33333 35114828 6186.833 2351.583 2419.167 2099 2216.5 [6,] 30407.50 39363.0 64.30000 35849554 6396.000 2418.500 2512.000 2188 2299.0 YAC25 YAC26 YAC27 YAC28 YAC29 YAD1 YAD2 YAD3 [1,] 3319.417 937.6667 1639 2406.917 2086.083 140.3 36659.21 299.9737 [2,] 3473.833 984.3333 1729 2522.833 2127.167 138.6 36818.42 301.9474 [3,] 3628.250 1031.0000 1819 2638.750 2168.250 136.9 36977.63 303.9211 [4,] 3782.667 1077.6667 1909 2754.667 2209.333 135.2 37136.84 305.8947 [5,] 3937.083 1124.3333 1999 2870.583 2250.417 133.5 37296.05 307.8684 [6,] 4091.500 1171.0000 2089 2986.500 2291.500 131.8 37455.26 309.8421 YAD4 YAD5 YAD6 YAD7 YAD8 YAD9 YAD10 YAD11 [1,] 1480.875 522.6316 495.1579 490.1053 985.2632 938.0526 1019.395 4178.429 [2,] 1415.750 523.2632 498.3158 493.2105 991.5263 939.1053 1020.789 4268.857 [3,] 1350.625 523.8947 501.4737 496.3158 997.7895 940.1579 1022.184 4359.286 [4,] 1285.500 524.5263 504.6316 499.4211 1004.0526 941.2105 1023.579 4449.714 [5,] 1220.375 525.1579 507.7895 502.5263 1010.3158 942.2632 1024.974 4540.143 [6,] 1155.250 525.7895 510.9474 505.6316 1016.5789 943.3158 1026.368 4630.571 YAD12 YAD13 YAD14 YAD15 YAD16 YAD17 YAD18 YAD19 [1,] 36.82857 39.75714 946.7143 23.0125 9.2625 414118.2 2.339091 1576652 [2,] 36.55714 39.71429 930.4286 22.8250 9.2250 415236.3 2.328182 1575943 [3,] 36.28571 39.67143 914.1429 22.6375 9.1875 416354.5 2.317273 1575235 [4,] 36.01429 39.62857 897.8571 22.4500 9.1500 417472.6 2.306364 1574526 [5,] 35.74286 39.58571 881.5714 22.2625 9.1125 418590.8 2.295455 1573818 [6,] 35.47143 39.54286 865.2857 22.0750 9.0750 419708.9 2.284545 1573109 YAD20 YAD21 YAD22 YAD23 YAD24 YAD25 YAD26 YAD27 [1,] 666.3333 26604.5 476.2353 449.1176 335793.7 28127.57 325039.1 10123.182 [2,] 693.6667 26768.0 479.4706 452.2353 337993.3 28260.14 327674.2 9992.364 [3,] 721.0000 26931.5 482.7059 455.3529 340193.0 28392.71 330309.2 9861.545 [4,] 748.3333 27095.0 485.9412 458.4706 342392.7 28525.29 332944.3 9730.727 [5,] 775.6667 27258.5 489.1765 461.5882 344592.3 28657.86 335579.4 9599.909 [6,] 803.0000 27422.0 492.4118 464.7059 346792.0 28790.43 338214.5 9469.091 YAD28 YAD29 YAD30 [1,] 7764.909 56.51762 1037.524 [2,] 7708.818 56.54524 1059.048 [3,] 7652.727 56.57286 1080.571 [4,] 7596.636 56.60048 1102.095 [5,] 7540.545 56.62810 1123.619 [6,] 7484.455 56.65571 1145.143 $forecasts$theta YAF2 YAF3 YAF4 YAF5 YAF6 YAF7 YAF8 YAF9 [1,] 565938.8 394342.6 370630.6 343795.6 19501512 15253.27 876501.3 653956.4 [2,] 578486.4 404640.6 379052.1 351953.9 19800960 15535.55 905299.5 669620.9 [3,] 591034.0 414938.7 387473.7 360112.2 20100408 15817.82 934097.6 685285.4 [4,] 603581.5 425236.7 395895.2 368270.5 20399856 16100.09 962895.8 700949.8 [5,] 616129.1 435534.8 404316.7 376428.8 20699304 16382.36 991694.0 716614.3 [6,] 628676.6 445832.8 412738.3 384587.1 20998752 16664.63 1020492.1 732278.8 YAF10 YAF11 YAF12 YAF13 YAF14 YAF15 YAF16 YAF17 [1,] 883950.0 54.48800 8602.318 1740132 50890.50 892079.5 1066.141 8.675195 [2,] 905774.4 55.04627 8757.663 1768449 51357.94 917899.2 1090.382 8.766434 [3,] 927598.9 55.60454 8913.008 1796766 51825.38 943718.9 1114.624 8.857672 [4,] 949423.3 56.16282 9068.353 1825084 52292.81 969538.6 1138.865 8.948911 [5,] 971247.7 56.72109 9223.697 1853401 52760.25 995358.3 1163.106 9.040150 [6,] 993072.1 57.27937 9379.042 1881718 53227.69 1021178.0 1187.347 9.131389 YAM1 YAM2 YAM3 YAM4 YAM5 YAM6 YAM7 YAM8 [1,] 73291.67 681863.6 6979.968 18649.32 25.68650 2.746527 1977.154 74.96959 [2,] 74512.34 697517.8 7103.413 19159.38 24.47304 2.752745 2034.888 73.49074 [3,] 75733.00 713172.0 7226.858 19669.45 23.25957 2.758962 2092.622 72.01190 [4,] 76953.66 728826.2 7350.302 20179.51 22.04611 2.765180 2150.356 70.53305 [5,] 78174.32 744480.4 7473.747 20689.57 20.83265 2.771398 2208.090 69.05420 [6,] 79394.99 760134.7 7597.191 21199.63 19.61919 2.777616 2265.824 67.57536 YAM10 YAM11 YAM12 YAM13 YAM14 YAM15 YAM16 YAM17 [1,] 54.34051 20671228 13184439 2257.787 816.1503 782.2875 93.11495 206.8584 [2,] 50.88102 20817357 13220250 2243.603 821.2954 787.3863 92.47234 210.5705 [3,] 47.42154 20963486 13256061 2229.419 826.4406 792.4851 91.82974 214.2826 [4,] 43.96205 21109614 13291872 2215.235 831.5857 797.5839 91.18714 217.9946 [5,] 40.50256 21255743 13327683 2201.051 836.7308 802.6827 90.54453 221.7067 [6,] 37.04308 21401872 13363495 2186.867 841.8759 807.7816 89.90193 225.4188 YAM18 YAM19 YAM20 YAM21 YAM22 YAM23 YAM24 YAM25 [1,] 5673.578 97.12819 9417.815 194.7614 102.9002 12254.22 9204.983 11761.79 [2,] 5765.155 97.06765 9452.625 195.2150 103.0006 12455.54 9359.926 11897.56 [3,] 5856.732 97.00712 9487.436 195.6686 103.1011 12656.86 9514.870 12033.33 [4,] 5948.309 96.94659 9522.246 196.1222 103.2015 12858.17 9669.813 12169.11 [5,] 6039.885 96.88606 9557.057 196.5758 103.3020 13059.49 9824.757 12304.88 [6,] 6131.462 96.82553 9591.867 197.0293 103.4024 13260.81 9979.700 12440.65 YAM26 YAM27 YAM28 YAM29 YAM30 YAB1 YAB2 YAB3 [1,] 25668.04 571.5277 1241.935 8036.742 75257.06 30346.08 7663.178 604340.6 [2,] 25928.03 584.0608 1264.882 8038.541 75848.96 30883.32 7771.421 620210.5 [3,] 26188.01 596.5939 1287.830 8040.340 76440.86 31420.57 7879.665 636080.4 [4,] 26448.00 609.1270 1310.777 8042.139 77032.76 31957.82 7987.908 651950.3 [5,] 26707.98 621.6601 1333.725 8043.938 77624.66 32495.06 8096.152 667820.2 [6,] 26967.97 634.1933 1356.672 8045.737 78216.56 33032.31 8204.396 683690.1 YAB4 YAB5 YAB6 YAB7 YAB8 YAB9 YAB10 YAB11 [1,] 78927.45 10382.87 748.2557 705557.0 181028.7 239738.6 40489.41 145355.8 [2,] 79915.56 10580.70 756.3650 719013.6 181947.6 249692.3 41880.88 148553.4 [3,] 80903.68 10778.54 764.4743 732470.3 182866.4 259645.9 43272.35 151751.1 [4,] 81891.79 10976.37 772.5836 745926.9 183785.3 269599.6 44663.83 154948.8 [5,] 82879.90 11174.21 780.6929 759383.6 184704.2 279553.2 46055.30 158146.5 [6,] 83868.01 11372.05 788.8022 772840.2 185623.0 289506.8 47446.77 161344.2 YAB12 YAI1 YAI2 YAI3 YAI4 YAI5 YAI6 YAI7 [1,] 26369.36 1221.070 39449.62 218.8794 2953.240 758.9790 1884202 22043151 [2,] 26434.73 1251.151 39723.07 220.6451 2977.327 761.9433 1908552 22286045 [3,] 26500.10 1281.233 39996.52 222.4108 3001.415 764.9076 1932901 22528939 [4,] 26565.46 1311.315 40269.98 224.1765 3025.503 767.8719 1957251 22771832 [5,] 26630.83 1341.396 40543.43 225.9423 3049.590 770.8362 1981601 23014726 [6,] 26696.20 1371.478 40816.88 227.7080 3073.678 773.8006 2005950 23257620 YAI8 YAI9 YAI10 YAI11 YAI12 YAI13 YAI14 YAI15 [1,] 8727.335 279.9258 214690.8 640.2527 1517.996 1059.778 836.3190 253.6565 [2,] 8839.913 289.8530 217242.1 651.6170 1563.793 1081.188 862.5558 260.2159 [3,] 8952.491 299.7803 219793.4 662.9812 1609.590 1102.597 888.7927 266.7753 [4,] 9065.069 309.7076 222344.6 674.3455 1655.387 1124.007 915.0295 273.3347 [5,] 9177.648 319.6349 224895.9 685.7097 1701.184 1145.416 941.2663 279.8941 [6,] 9290.226 329.5621 227447.2 697.0739 1746.980 1166.826 967.5031 286.4535 YAI16 YAI17 YAI18 YAI19 YAI20 YAI21 YAI22 YAI23 [1,] 142.6639 1302.162 113.8894 38.72376 13.81705 1241.935 3170.028 24.17445 [2,] 146.1278 1332.146 112.9055 39.24739 13.71592 1264.882 3223.635 24.21547 [3,] 149.5916 1362.131 111.9216 39.77101 13.61478 1287.830 3277.241 24.25648 [4,] 153.0554 1392.115 110.9377 40.29464 13.51365 1310.777 3330.847 24.29750 [5,] 156.5193 1422.099 109.9538 40.81826 13.41252 1333.725 3384.454 24.33851 [6,] 159.9831 1452.083 108.9699 41.34189 13.31139 1356.672 3438.060 24.37953 YAI24 YAI25 YAI26 YAI27 YAI28 YAI29 YAI30 YAI31 [1,] 133170.8 58.14310 525.2985 3942.519 380.6816 147.3531 16.83749 6.507065 [2,] 135147.5 59.52002 533.9327 4045.041 389.6629 150.1061 17.33515 6.634040 [3,] 137124.2 60.89694 542.5669 4147.563 398.6442 152.8592 17.83282 6.761016 [4,] 139100.9 62.27385 551.2011 4250.085 407.6256 155.6122 18.33048 6.887991 [5,] 141077.6 63.65077 559.8353 4352.607 416.6069 158.3653 18.82815 7.014967 [6,] 143054.3 65.02769 568.4696 4455.129 425.5882 161.1183 19.32581 7.141942 YAI32 YAI33 YAI34 YAI35 YAG1 YAG2 YAG3 YAG4 [1,] 14.30276 8.056203 3.387901 2.856823 241.4434 53.08375 86.71936 11.48687 [2,] 14.40550 8.071011 3.440264 2.861630 245.2879 53.64765 88.77922 11.83379 [3,] 14.50825 8.085819 3.492628 2.866438 249.1325 54.21155 90.83908 12.18071 [4,] 14.61100 8.100626 3.544991 2.871246 252.9771 54.77545 92.89894 12.52764 [5,] 14.71375 8.115434 3.597355 2.876053 256.8217 55.33936 94.95881 12.87456 [6,] 14.81649 8.130242 3.649719 2.880861 260.6663 55.90326 97.01867 13.22148 YAG5 YAG6 YAG7 YAG8 YAG9 YAG10 YAG11 YAG12 [1,] 116.8489 110.2695 113.6728 188.5472 126.0000 94.10021 363299.0 109407.1 [2,] 118.6982 113.1576 113.8268 189.0959 126.0007 95.80066 370043.2 111576.9 [3,] 120.5475 116.0457 113.9808 189.6446 126.0015 97.50111 376787.5 113746.6 [4,] 122.3967 118.9338 114.1347 190.1933 126.0023 99.20156 383531.8 115916.4 [5,] 124.2460 121.8219 114.2887 190.7421 126.0030 100.90202 390276.1 118086.1 [6,] 126.0953 124.7099 114.4427 191.2908 126.0038 102.60247 397020.3 120255.9 YAG13 YAG14 YAG15 YAG16 YAG17 YAG18 YAG19 YAG20 [1,] 95625.57 2441.397 30887.95 468320.4 42.03434 613.4947 583.9121 863.2322 [2,] 97300.80 2296.987 31498.02 476763.4 42.64887 628.9947 598.8265 868.3661 [3,] 98976.03 2152.578 32108.08 485206.4 43.26340 644.4947 613.7408 873.5001 [4,] 100651.26 2008.169 32718.14 493649.4 43.87793 659.9947 628.6551 878.6341 [5,] 102326.49 1863.759 33328.21 502092.5 44.49246 675.4947 643.5695 883.7680 [6,] 104001.71 1719.350 33938.27 510535.5 45.10699 690.9947 658.4838 888.9020 YAG21 YAG22 YAG23 YAG24 YAG25 YAG26 YAG27 YAG28 [1,] 5.692489 10.29121 134.5414 64.33905 22.45877 11.46493 6.117998 7.527294 [2,] 5.784989 10.48246 137.5834 65.57816 22.81770 11.62993 6.236033 7.654616 [3,] 5.877489 10.67371 140.6254 66.81727 23.17663 11.79493 6.354069 7.781937 [4,] 5.969989 10.86496 143.6673 68.05637 23.53556 11.95993 6.472105 7.909258 [5,] 6.062489 11.05621 146.7093 69.29548 23.89449 12.12493 6.590140 8.036580 [6,] 6.154989 11.24746 149.7513 70.53459 24.25342 12.28993 6.708176 8.163901 YAG29 YAG30 YAC1 YAC2 YAC3 YAC4 YAC5 YAC6 [1,] 7.810328 4.267834 75.49496 28.08939 18.03963 22.73670 97.07023 20.03551 [2,] 7.920685 4.335691 76.48015 28.52898 18.37933 23.38363 98.49098 20.24054 [3,] 8.031042 4.403548 77.46534 28.96857 18.71903 24.03055 99.91172 20.44557 [4,] 8.141400 4.471405 78.45053 29.40815 19.05872 24.67747 101.33246 20.65059 [5,] 8.251757 4.539262 79.43573 29.84774 19.39842 25.32440 102.75320 20.85562 [6,] 8.362114 4.607120 80.42092 30.28733 19.73812 25.97132 104.17394 21.06065 YAC7 YAC8 YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 [1,] 33.04683 26.11871 39.90827 74401.61 32265.50 53079.34 39696.94 53836.62 [2,] 33.40384 26.60762 40.88681 75021.38 32671.14 54323.88 40309.99 54723.56 [3,] 33.76084 27.09652 41.86536 75641.16 33076.77 55568.42 40923.04 55610.49 [4,] 34.11785 27.58542 42.84390 76260.93 33482.41 56812.96 41536.09 56497.42 [5,] 34.47485 28.07432 43.82244 76880.71 33888.05 58057.50 42149.14 57384.35 [6,] 34.83186 28.56322 44.80099 77500.48 34293.68 59302.04 42762.19 58271.28 YAC15 YAC16 YAC17 YAC18 YAC19 YAC20 YAC21 YAC22 [1,] 55694.15 26475.44 32479.94 53.45285 31785389 5242.704 2052.823 2000.253 [2,] 57100.60 26814.54 33022.26 54.40587 32129671 5344.422 2088.648 2045.519 [3,] 58507.04 27153.64 33564.57 55.35889 32473952 5446.139 2124.472 2090.786 [4,] 59913.48 27492.75 34106.89 56.31191 32818233 5547.856 2160.296 2136.052 [5,] 61319.92 27831.85 34649.21 57.26494 33162514 5649.573 2196.120 2181.319 [6,] 62726.37 28170.96 35191.52 58.21796 33506796 5751.290 2231.944 2226.585 YAC23 YAC24 YAC25 YAC26 YAC27 YAC28 YAC29 YAD1 [1,] 1702.062 1830.056 3241.379 909.6797 1593.560 2355.935 2073.892 109.3342 [2,] 1750.128 1856.122 3317.772 928.3638 1638.129 2420.855 2102.779 108.8524 [3,] 1798.194 1882.188 3394.165 947.0479 1682.698 2485.775 2131.666 108.3706 [4,] 1846.260 1908.254 3470.558 965.7319 1727.266 2550.696 2160.554 107.8887 [5,] 1894.326 1934.320 3546.951 984.4160 1771.835 2615.616 2189.441 107.4069 [6,] 1942.392 1960.386 3623.343 1003.1001 1816.404 2680.536 2218.329 106.9251 YAD2 YAD3 YAD4 YAD5 YAD6 YAD7 YAD8 YAD9 [1,] 36580.69 297.3869 1693.233 490.2888 450.0180 446.6219 896.5404 885.0943 [2,] 36661.39 298.0967 1668.324 490.0699 450.6517 447.2972 897.8461 884.7548 [3,] 36742.10 298.8066 1643.416 489.8511 451.2854 447.9725 899.1518 884.4153 [4,] 36822.80 299.5164 1618.508 489.6323 451.9191 448.6478 900.4574 884.0759 [5,] 36903.50 300.2262 1593.599 489.4135 452.5528 449.3231 901.7631 883.7364 [6,] 36984.20 300.9360 1568.691 489.1946 453.1865 449.9984 903.0688 883.3969 YAD10 YAD11 YAD12 YAD13 YAD14 YAD15 YAD16 YAD17 [1,] 955.7087 3425.193 37.02926 40.13699 995.3581 23.10254 9.418605 412398.4 [2,] 955.3723 3413.709 36.92033 40.16931 989.3143 23.00504 9.419439 412948.2 [3,] 955.0358 3402.225 36.81140 40.20163 983.2706 22.90754 9.420272 413498.0 [4,] 954.6994 3390.741 36.70247 40.23395 977.2268 22.81004 9.421105 414047.8 [5,] 954.3629 3379.257 36.59354 40.26627 971.1831 22.71254 9.421939 414597.6 [6,] 954.0265 3367.773 36.48461 40.29860 965.1393 22.61504 9.422772 415147.4 YAD18 YAD19 YAD20 YAD21 YAD22 YAD23 YAD24 YAD25 [1,] 2.328401 1548110 651.7109 26525.37 469.5552 442.8445 328772.6 28062.50 [2,] 2.323576 1544977 664.4261 26609.75 469.1941 442.5369 329724.3 28130.01 [3,] 2.318750 1541844 677.1412 26694.13 468.8329 442.2294 330676.0 28197.53 [4,] 2.313925 1538711 689.8564 26778.51 468.4717 441.9219 331627.7 28265.04 [5,] 2.309100 1535578 702.5715 26862.89 468.1105 441.6143 332579.4 28332.55 [6,] 2.304275 1532445 715.2867 26947.27 467.7493 441.3068 333531.1 28400.06 YAD26 YAD27 YAD28 YAD29 YAD30 [1,] 315589.0 10219.71 7799.905 56.20913 1038.892 [2,] 316663.8 10185.34 7778.780 56.21254 1050.531 [3,] 317738.6 10150.97 7757.656 56.21596 1062.170 [4,] 318813.5 10116.60 7736.532 56.21937 1073.808 [5,] 319888.3 10082.23 7715.408 56.22278 1085.447 [6,] 320963.2 10047.86 7694.284 56.22620 1097.086 $forecasts$nn YAF2 YAF3 YAF4 YAF5 YAF6 YAF7 YAF8 YAF9 [1,] 575492.7 399629.9 369193.7 310629.4 19428039 14894.29 872037.9 691912.8 [2,] 592589.0 407195.2 373779.0 297390.3 19889536 14846.82 874910.3 761425.9 [3,] 605377.6 410557.5 376714.1 291765.6 20187276 14820.20 875195.9 849688.5 [4,] 614691.8 411990.2 378562.1 289172.1 20371966 14805.18 875223.7 951355.1 [5,] 621339.6 412589.4 379713.4 287933.5 20483654 14796.68 875226.4 1046252.8 [6,] 626014.5 412838.0 380426.0 287332.3 20550137 14791.86 875226.7 1111500.3 YAF10 YAF11 YAF12 YAF13 YAF14 YAF15 YAF16 YAF17 [1,] 885477.9 52.69249 8857.873 1901987 50529.13 861090.0 1051.584 8.706654 [2,] 891005.6 52.14200 9165.724 2091790 50596.97 858333.5 1053.548 8.812083 [3,] 892095.8 51.87795 9379.898 2269781 50640.25 856917.5 1053.925 8.901062 [4,] 892302.0 51.74696 9520.677 2425345 50667.81 856187.3 1053.996 8.974965 [5,] 892340.7 51.68090 9609.593 2551890 50685.35 855810.0 1054.010 9.035502 [6,] 892348.0 51.64732 9664.292 2648236 50696.50 855614.8 1054.013 9.084514 YAM1 YAM2 YAM3 YAM4 YAM5 YAM6 YAM7 YAM8 [1,] 67950.72 527730.9 6872.628 19042.64 26.84317 2.751186 2026.672 88.98394 [2,] 65367.04 519972.9 6882.874 19116.32 26.83098 2.760801 2104.403 88.98431 [3,] 63580.89 519041.7 6889.336 19121.17 26.82838 2.768942 2154.513 88.98431 [4,] 62331.62 518924.1 6893.397 19121.48 26.82783 2.775557 2184.088 88.98431 [5,] 61450.96 518909.1 6895.943 19121.50 26.82771 2.780736 2200.563 88.98431 [6,] 60826.79 518907.2 6897.538 19121.50 26.82769 2.784665 2209.431 88.98431 YAM10 YAM11 YAM12 YAM13 YAM14 YAM15 YAM16 YAM17 [1,] 66.68495 19830958 12759930 2789.753 807.8267 787.2334 99.08720 150.9095 [2,] 74.99940 19173689 12678303 2738.660 806.2759 797.1793 98.55941 150.8903 [3,] 79.76851 18595928 12653672 2735.203 805.4976 801.1426 98.44522 150.8903 [4,] 81.61698 18124729 12646019 2734.971 805.1019 802.4352 98.42289 150.8903 [5,] 81.97246 17765865 12643617 2734.955 804.8995 802.8257 98.41862 150.8903 [6,] 81.82049 17507723 12642861 2734.954 804.7955 802.9407 98.41781 150.8903 YAM18 YAM19 YAM20 YAM21 YAM22 YAM23 YAM24 YAM25 [1,] 5777.606 98.54976 8883.975 199.9107 101.21213 12445.71 9197.850 11467.08 [2,] 5940.689 98.54983 8182.169 170.2668 107.49635 12732.66 9270.385 11424.29 [3,] 6070.535 98.54983 7977.572 145.7209 104.53110 12931.90 9304.311 11411.76 [4,] 6169.863 98.54983 7846.537 183.6302 91.53446 13065.09 9319.815 11408.01 [5,] 6243.400 98.54983 7667.892 164.9640 83.10465 13151.79 9326.823 11406.88 [6,] 6296.471 98.54983 7632.914 181.7179 86.55697 13207.23 9329.975 11406.54 YAM26 YAM27 YAM28 YAM29 YAM30 YAB1 YAB2 YAB3 [1,] 24888.14 599.2752 1317.857 8068.125 59460.35 31865.68 7504.441 494040.1 [2,] 24788.67 630.9691 1406.641 8106.665 58306.24 34085.25 7435.358 488630.5 [3,] 24766.08 654.2547 1480.632 8151.551 58123.32 36454.87 7426.270 488061.6 [4,] 24760.78 670.4402 1538.025 8203.846 58092.34 38942.79 7428.204 487999.4 [5,] 24759.52 681.2356 1579.857 8264.746 58087.04 41494.74 7428.999 487992.5 [6,] 24759.22 688.2307 1608.877 8335.529 58086.13 44034.55 7429.039 487991.8 YAB4 YAB5 YAB6 YAB7 YAB8 YAB9 YAB10 YAB11 [1,] 63225.79 10181.66 728.4000 692682.6 150290.5 284913.8 38073.22 141505.5 [2,] 57964.45 10180.39 646.1448 692811.2 150552.1 352537.8 37583.07 141505.5 [3,] 55800.81 10179.90 653.4898 692839.6 150733.4 425033.1 37341.39 141505.5 [4,] 54822.64 10179.71 648.9781 692845.8 150929.5 486449.2 37220.47 141505.5 [5,] 54362.61 10179.64 649.2445 692847.2 151240.9 525347.8 37159.53 141505.5 [6,] 54142.35 10179.61 649.1851 692847.5 152073.8 544509.8 37128.70 141505.5 YAB12 YAI1 YAI2 YAI3 YAI4 YAI5 YAI6 YAI7 [1,] 26110.34 1367.665 32630.58 292.3572 2544.847 741.1849 1927374 22337647 [2,] 26110.01 1565.225 32630.58 183.3336 2335.393 734.4500 1987297 22758194 [3,] 26110.01 1767.706 32630.58 135.2681 2217.012 731.1947 2039196 23078760 [4,] 26110.01 1950.679 32630.58 254.5747 2144.847 729.5763 2083140 23318082 [5,] 26110.01 2093.037 32630.58 272.8503 2098.926 728.7608 2119606 23493910 [6,] 26110.01 2188.817 32630.58 222.3718 2068.928 728.3470 2149340 23621542 YAI8 YAI9 YAI10 YAI11 YAI12 YAI13 YAI14 YAI15 [1,] 6937.787 291.8314 214355.1 652.2356 1528.419 1563.553 953.3381 268.3191 [2,] 6937.730 311.1202 215080.8 673.7948 1564.430 2129.507 1044.4228 291.0934 [3,] 6937.730 326.9322 215299.0 697.6634 1586.358 2361.668 1089.6489 314.7506 [4,] 6937.730 338.9875 215362.8 724.2685 1599.282 2399.531 1108.9186 338.2332 [5,] 6937.730 347.6189 215381.3 754.0601 1606.750 2404.006 1116.5421 360.2492 [6,] 6937.730 353.5007 215386.6 787.4682 1611.015 2404.509 1119.4654 379.5913 YAI16 YAI17 YAI18 YAI19 YAI20 YAI21 YAI22 YAI23 [1,] 141.8073 1236.909 118.3608 38.19212 14.61940 1315.960 3283.556 22.52807 [2,] 142.3412 1220.932 118.3610 38.18810 15.07187 1401.744 3378.348 21.81379 [3,] 142.4433 1213.290 118.3610 38.18605 15.28020 1471.975 3421.021 22.07716 [4,] 142.4626 1209.541 118.3610 38.18500 15.32003 1525.427 3437.937 25.69834 [5,] 142.4662 1207.681 118.3610 38.18446 15.47744 1563.662 3444.277 24.27430 [6,] 142.4669 1206.751 118.3610 38.18419 16.53902 1589.727 3446.602 21.85865 YAI24 YAI25 YAI26 YAI27 YAI28 YAI29 YAI30 YAI31 [1,] 135351.7 60.35571 461.9940 3917.467 370.2823 140.8874 18.69895 6.580538 [2,] 138070.1 61.85554 461.9316 3948.510 369.5409 139.9295 22.21512 6.630731 [3,] 139722.4 62.36335 461.9312 3960.435 369.1500 139.6550 27.29116 6.638319 [4,] 140679.8 62.52058 461.9312 3964.939 368.9432 139.5742 33.15172 6.639343 [5,] 141218.6 62.56782 461.9312 3966.629 368.8335 139.5502 37.18205 6.639479 [6,] 141516.7 62.58189 461.9312 3967.262 368.7753 139.5430 38.65363 6.639496 YAI32 YAI33 YAI34 YAI35 YAG1 YAG2 YAG3 YAG4 [1,] 14.20655 0.6007721 3.436084 2.798442 255.6436 53.79382 90.41556 -7.232282 [2,] 14.20655 8.0923714 3.455013 2.928060 277.0345 55.49592 94.46789 -4.004830 [3,] 14.20655 8.0508661 3.458184 2.810519 299.7317 57.85855 96.97483 -19.960397 [4,] 14.20655 8.0636020 3.458701 2.864241 319.7078 61.21416 98.38972 2.869908 [5,] 14.20655 8.0601756 3.458785 2.811361 333.6176 65.86342 99.14427 2.853248 [6,] 14.20655 8.0611355 3.458799 2.927093 341.4161 71.46569 99.53405 14.850396 YAG5 YAG6 YAG7 YAG8 YAG9 YAG10 YAG11 YAG12 [1,] 117.4432 117.5871 138.0308 205.0734 125.87031 94.01107 369419.5 116056.1 [2,] 118.7935 130.1082 250.6215 228.1269 119.61734 95.43309 379842.7 127523.3 [3,] 119.4856 145.8963 323.6132 258.9059 108.48954 96.67468 387699.4 142896.8 [4,] 119.8260 164.1115 323.6146 297.5468 96.59816 97.74800 393267.9 160221.5 [5,] 119.9898 181.0312 323.6146 339.2464 88.62641 98.66762 397030.5 172356.3 [6,] 120.0679 192.3724 323.6146 373.9047 85.03938 99.44934 399486.9 176965.8 YAG13 YAG14 YAG15 YAG16 YAG17 YAG18 YAG19 YAG20 [1,] 91832.17 6391.388 27724.49 477102.0 36.66592 603.8993 575.7030 868.9144 [2,] 90882.80 6393.135 27555.21 490382.1 36.36350 605.1263 576.7579 878.3167 [3,] 90428.43 6393.194 27533.47 500070.0 36.31856 605.3693 576.9137 886.3495 [4,] 90204.38 6393.196 27530.54 506566.0 36.31143 605.4169 576.9365 893.1056 [5,] 90092.31 6393.196 27530.14 510655.2 36.31028 605.4262 576.9398 898.7111 [6,] 90035.86 6393.196 27530.09 513121.2 36.31010 605.4281 576.9403 903.3080 YAG21 YAG22 YAG23 YAG24 YAG25 YAG26 YAG27 YAG28 [1,] 5.835398 10.45697 133.9129 64.33596 23.57807 11.51081 6.477270 7.413244 [2,] 6.051056 10.76028 135.3869 64.99750 25.18304 11.62774 6.948301 7.417990 [3,] 6.231276 11.00567 136.2519 65.32900 26.82040 11.68840 7.364609 7.419675 [4,] 6.368420 11.19561 136.7473 65.48938 28.35112 11.71873 7.689336 7.420272 [5,] 6.464461 11.33730 137.0270 65.56561 29.63947 11.73361 7.914286 7.420482 [6,] 6.527468 11.43993 137.1835 65.60155 30.61255 11.74084 8.055920 7.420557 YAG29 YAG30 YAC1 YAC2 YAC3 YAC4 YAC5 YAC6 [1,] 8.052094 4.462523 77.52834 29.81011 17.55137 24.84738 99.6737 20.72075 [2,] 8.356963 4.695836 80.66959 32.47578 17.51471 27.47893 103.7684 20.82462 [3,] 8.592950 4.877940 83.75118 35.50205 17.50531 29.65096 107.7277 20.61923 [4,] 8.757572 5.003452 86.55002 38.39748 17.50288 31.18702 111.3168 20.37554 [5,] 8.863234 5.081709 88.87875 40.55814 17.50225 32.13768 114.3439 20.44966 [6,] 8.927175 5.127210 90.65459 41.80326 17.50208 32.67248 116.7202 20.62694 YAC7 YAC8 YAC9 YAC10 YAC11 YAC12 YAC13 YAC14 [1,] 33.31962 26.56871 42.46983 77941.28 32844.51 54436.20 35706.36 48484.07 [2,] 33.96389 26.78407 45.30003 83991.87 33460.14 56754.15 35287.12 47185.81 [3,] 34.60990 26.82460 47.24928 88723.96 33778.48 58703.60 35217.94 46785.51 [4,] 35.23768 26.83191 48.43649 90079.23 33924.77 60253.44 35205.85 46659.96 [5,] 35.82310 26.83321 49.10053 90277.85 33988.05 61425.33 35203.72 46620.38 [6,] 36.34324 26.83344 49.45321 90302.41 34014.68 62275.55 35203.35 46607.88 YAC15 YAC16 YAC17 YAC18 YAC19 YAC20 YAC21 YAC22 [1,] 57963.74 24468.49 28906.88 54.60490 32188754 5218.686 2036.696 2069.828 [2,] 60861.07 24392.62 28906.87 56.47057 32817348 5280.281 2048.756 2153.877 [3,] 62924.77 24386.11 28906.87 58.01514 33333636 5328.372 2055.953 2208.896 [4,] 64278.13 24385.53 28906.87 59.21213 33749176 5365.453 2060.182 2242.033 [5,] 65114.21 24385.48 28906.87 60.08769 34078001 5393.761 2062.643 2260.928 [6,] 65610.78 24385.47 28906.87 60.69917 34334627 5415.204 2064.067 2271.352 YAC23 YAC24 YAC25 YAC26 YAC27 YAC28 YAC29 YAD1 [1,] 1649.442 1840.361 3348.527 957.872 1680.046 2319.918 2047.014 119.8065 [2,] 1647.817 1880.932 3490.033 1043.045 1792.937 2334.792 2047.963 107.3122 [3,] 1647.232 1927.401 3588.411 1153.308 1880.997 2342.219 2048.003 107.2456 [4,] 1647.021 1982.080 3651.394 1294.209 1943.713 2345.872 2047.966 107.2456 [5,] 1646.945 2048.233 3689.440 1461.966 1985.225 2347.655 2047.959 107.2456 [6,] 1646.917 2130.543 3711.580 1631.767 2011.285 2348.522 2047.960 107.2456 YAD2 YAD3 YAD4 YAD5 YAD6 YAD7 YAD8 YAD9 [1,] 36516.98 292.1441 2065.333 505.2602 428.1054 421.9509 849.7234 881.7086 [2,] 36531.09 287.6680 1989.222 481.2276 426.1989 420.9042 846.8517 855.7625 [3,] 36542.80 284.2131 2065.328 472.8581 425.8693 420.7787 846.4326 846.2399 [4,] 36552.50 281.5441 1989.283 483.7794 425.8073 420.7628 846.3669 886.4371 [5,] 36560.53 279.4889 2065.328 483.8930 425.7954 420.7607 846.3564 863.6140 [6,] 36567.16 277.9140 1989.284 488.8397 425.7931 420.7604 846.3548 890.9700 YAD10 YAD11 YAD12 YAD13 YAD14 YAD15 YAD16 YAD17 [1,] 966.1360 4023.264 36.92078 39.90756 1129.880 23.21975 9.424923 411163.0 [2,] 903.7045 4023.240 36.89937 39.90926 1348.409 23.21981 9.423143 409649.6 [3,] 890.8418 4023.240 36.89767 39.90930 1562.706 23.21981 9.423397 408225.8 [4,] 951.0978 4023.240 36.89754 39.90930 1707.191 23.21981 9.423363 406750.3 [5,] 947.1832 4023.240 36.89753 39.90930 1776.377 23.21981 9.423367 405102.0 [6,] 981.5836 4023.240 36.89753 39.90930 1803.141 23.21981 9.423367 403153.5 YAD18 YAD19 YAD20 YAD21 YAD22 YAD23 YAD24 YAD25 [1,] 2.303649 1574189 673.5461 26529.98 471.4621 446.4357 325495.6 28109.04 [2,] 2.303649 1572028 683.7740 26578.76 463.1851 448.5442 325495.6 28188.56 [3,] 2.303649 1570414 685.8379 26603.95 435.9889 457.0289 325495.6 28240.44 [4,] 2.303649 1569138 686.2127 26616.54 432.6536 467.7921 325495.6 28272.73 [5,] 2.303649 1568083 686.2793 26622.73 432.6534 468.4836 325495.6 28292.22 [6,] 2.303649 1567184 686.2911 26625.74 432.6534 468.4872 325495.6 28303.76 YAD26 YAD27 YAD28 YAD29 YAD30 [1,] 310255.5 5973.464 6650.774 56.08189 1030.702 [2,] 310254.8 3734.677 5348.192 55.69903 1042.948 [3,] 310254.7 3734.647 5337.048 55.39515 1052.661 [4,] 310254.7 3734.647 5337.047 55.19532 1060.031 [5,] 310254.7 3734.647 5337.047 55.08330 1065.421 [6,] 310254.7 3734.647 5337.047 55.02685 1069.248 ``` --- ## seer package: `prepare_trainingset` ```r prep_tset <- prepare_trainingset(accuracy_set = accuracy_m1, feature_set = features_m1) prep_tset ``` ``` $modelinfo # A tibble: 181 × 4 ARIMA_name ETS_name min_label model_names <chr> <chr> <chr> <chr> 1 ARIMA(0,1,0) with drift ETS(A,A,N) ets ETS(A,A,N) 2 ARIMA(0,1,1) with drift ETS(M,A,N) rwd rwd 3 ARIMA(0,1,2) with drift ETS(M,A,N) ets ETS(M,A,N) 4 ARIMA(1,1,0) with drift ETS(M,A,N) rwd rwd 5 ARIMA(0,1,1) with drift ETS(M,A,N) arima ARIMA(0,1,1) with drift 6 ARIMA(1,1,0) with drift ETS(M,A,N) ets ETS(M,A,N) 7 ARIMA(0,1,0) with drift ETS(M,N,N) rwd rwd 8 ARIMA(0,1,0) with drift ETS(A,N,N) nn nn 9 ARIMA(0,1,0) with drift ETS(M,N,N) rwd rwd 10 ARIMA(0,1,0) with drift ETS(M,A,N) theta theta # … with 171 more rows $trainingset # A tibble: 181 × 26 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> 1 0.442 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603 2 0.363 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272 3 0.379 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172 4 0.363 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396 5 0.156 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113 6 0.441 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385 7 0.118 0 0 0.943 0.975 4.95e-6 2.94 0.391 0.0868 8 0.357 0 0 0.949 0.978 2.39e-6 3.11 -0.360 0.220 9 0.698 0 0 0.931 0.983 5.09e-6 2.74 0.381 0.198 10 0.435 0.0188 1.05 0.987 0.956 8.44e-6 4.70 -1.57 0.445 # … with 171 more rows, and 17 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, # diff2y_acf1 <dbl>, y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, # nonlinearity <dbl>, lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>, # y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, # beta <dbl>, classlabels <chr> ``` --- ## seer package: `prepare_trainingset` ```r prep_tset$trainingset ``` ``` # A tibble: 181 × 26 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> 1 0.442 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603 2 0.363 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272 3 0.379 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172 4 0.363 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396 5 0.156 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113 6 0.441 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385 7 0.118 0 0 0.943 0.975 4.95e-6 2.94 0.391 0.0868 8 0.357 0 0 0.949 0.978 2.39e-6 3.11 -0.360 0.220 9 0.698 0 0 0.931 0.983 5.09e-6 2.74 0.381 0.198 10 0.435 0.0188 1.05 0.987 0.956 8.44e-6 4.70 -1.57 0.445 # … with 171 more rows, and 17 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, # diff2y_acf1 <dbl>, y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, # nonlinearity <dbl>, lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>, # y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, # beta <dbl>, classlabels <chr> ``` --- ## seer package ```r M3yearly_features <- seer::cal_features(yearly_m3, database="M3", h=6, highfreq = FALSE) head(M3yearly_features) ``` ``` # A tibble: 6 × 25 entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1 <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> 1 0.568 0 0 0.971 0.995 0.000000237 3.58 0.424 0.412 2 0.745 0 0 0.947 0.869 0.000179 2.05 -2.08 0.324 3 0.423 0 0 0.949 0.865 0.000193 1.75 -2.26 0.457 4 0.513 0 0 0.949 0.853 0.000368 2.87 -1.25 0.281 5 0.553 0 0 0.855 0.586 0.00127 -0.765 -1.77 0.192 6 0.709 0 0 0.964 0.964 0.0000217 3.56 -0.574 0.181 # … with 16 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, diff2y_acf1 <dbl>, # y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, nonlinearity <dbl>, # lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>, y_acf5 <dbl>, # diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, beta <dbl> ``` --- ## seer package: `build_rf` ```r rf <- build_rf(training_set = prep_tset$trainingset, testset=M3yearly_features, rf_type="rcp", ntree=100, seed=1, import=FALSE, mtry = 8) rf$predictions ``` ``` 1 2 3 ETS-trend rwd rwd 4 5 6 rwd rwd rwd 7 8 9 rwd rwd rwd 10 11 12 rwd rwd ARIMA 13 14 15 rwd rwd nn 16 17 18 rwd rwd rwd 19 20 21 rwd rwd rwd 22 23 24 rwd rwd rwd 25 26 27 nn rwd rwd 28 29 30 rwd rwd rwd 31 32 33 rwd ETS-trend rw 34 35 36 rwd rwd ARIMA 37 38 39 rwd ETS-trend ARIMA 40 41 42 ARIMA rwd ARIMA 43 44 45 ARIMA rwd rwd 46 47 48 rwd rwd ARIMA 49 50 51 rwd rwd rwd 52 53 54 ARIMA nn ETS-notrendnoseasonal 55 56 57 rwd rwd rwd 58 59 60 rwd rwd rwd 61 62 63 rwd rwd nn 64 65 66 rwd ETS-trend rwd 67 68 69 rwd rwd rwd 70 71 72 rwd rwd rwd 73 74 75 rwd rwd ARIMA 76 77 78 rwd theta rwd 79 80 81 rwd rwd rwd 82 83 84 rwd ETS-trend rwd 85 86 87 rwd rwd rwd 88 89 90 rwd rwd ETS-trend 91 92 93 rwd rwd ETS-trend 94 95 96 rwd rwd rwd 97 98 99 rwd rwd rwd 100 101 102 rwd rwd rwd 103 104 105 rwd rwd rwd 106 107 108 rwd rwd rwd 109 110 111 rwd rwd rwd 112 113 114 rwd rwd rwd 115 116 117 ARIMA rwd rwd 118 119 120 rwd rwd theta 121 122 123 rwd rwd ETS-notrendnoseasonal 124 125 126 rwd rwd rwd 127 128 129 rwd rwd rwd 130 131 132 ETS-notrendnoseasonal ARIMA rwd 133 134 135 rwd ARIMA rwd 136 137 138 rwd rw rwd 139 140 141 rwd rwd ETS-trend 142 143 144 ETS-notrendnoseasonal rwd rwd 145 146 147 rwd rwd rwd 148 149 150 rwd rwd rwd 151 152 153 rwd rwd rwd 154 155 156 rwd rwd ARIMA 157 158 159 ARIMA ARIMA ARIMA 160 161 162 rwd rwd rwd 163 164 165 rwd ARIMA ARIMA 166 167 168 rwd ARIMA ARIMA 169 170 171 ARIMA ARIMA ARIMA 172 173 174 ARIMA ARIMA ARIMA 175 176 177 ARIMA ARIMA rwd 178 179 180 rwd rwd rwd 181 182 183 ARIMA ARIMA ARIMA 184 185 186 ARIMA ARIMA ARIMA 187 188 189 ARIMA ARIMA ARIMA 190 191 192 ARIMA ARIMA rwd 193 194 195 rwd rwd rwd 196 197 198 rwd rwd rwd 199 200 201 rwd rwd rwd 202 203 204 rwd rwd rwd 205 206 207 rwd rwd rwd 208 209 210 rwd rwd rwd 211 212 213 rwd rwd rwd 214 215 216 rwd rwd rwd 217 218 219 rw rw rwd 220 221 222 rwd rwd rwd 223 224 225 rwd rwd rwd 226 227 228 rwd rwd rwd 229 230 231 rwd rwd rwd 232 233 234 rwd nn rwd 235 236 237 rwd rwd nn 238 239 240 rwd rwd rwd 241 242 243 rwd rwd nn 244 245 246 rwd rwd rwd 247 248 249 rwd rwd rwd 250 251 252 rwd ETS-trend rwd 253 254 255 ETS-trend ETS-trend rwd 256 257 258 ETS-trend rwd ETS-trend 259 260 261 rwd rwd rwd 262 263 264 rwd rwd rwd 265 266 267 rwd rwd rwd 268 269 270 rwd ETS-trend rwd 271 272 273 rwd nn rwd 274 275 276 rwd rwd ETS-trend 277 278 279 rwd rwd rwd 280 281 282 rwd rwd rwd 283 284 285 ETS-trend rwd rwd 286 287 288 ETS-trend rwd rwd 289 290 291 rwd ARIMA rwd 292 293 294 rwd rwd rwd 295 296 297 rwd rwd rwd 298 299 300 rwd rwd rwd 301 302 303 rwd rwd rwd 304 305 306 rwd rwd rwd 307 308 309 rwd rwd rwd 310 311 312 rwd rwd rwd 313 314 315 rwd rwd rwd 316 317 318 rwd rwd rwd 319 320 321 rwd rwd rwd 322 323 324 rwd rwd rwd 325 326 327 rwd rwd rwd 328 329 330 rwd rwd rwd 331 332 333 rwd ARIMA ARIMA 334 335 336 ARIMA ARIMA ARIMA 337 338 339 ARIMA rwd nn 340 341 342 rwd rwd rwd 343 344 345 rwd rwd rwd 346 347 348 rwd ARIMA ARIMA 349 350 351 ARIMA ARIMA rwd 352 353 354 rwd rwd rwd 355 356 357 rwd rwd rwd 358 359 360 rwd rwd rwd 361 362 363 rwd rwd rwd 364 365 366 rwd rwd ARIMA 367 368 369 rwd rwd rwd 370 371 372 ARMA/AR/MA rwd rwd 373 374 375 rwd rwd rwd 376 377 378 rwd rwd rwd 379 380 381 rwd rwd rwd 382 383 384 rwd rwd rwd 385 386 387 rwd rw rwd 388 389 390 rwd rwd ARIMA 391 392 393 ARIMA ARIMA rwd 394 395 396 rwd rwd rwd 397 398 399 rwd rwd rwd 400 401 402 rwd rwd rwd 403 404 405 nn rwd rwd 406 407 408 ARIMA rwd ARIMA 409 410 411 ARIMA rwd rwd 412 413 414 rwd rwd rwd 415 416 417 rwd rwd rwd 418 419 420 ARIMA rwd rwd 421 422 423 rwd rwd rwd 424 425 426 rwd rwd rwd 427 428 429 rwd rwd rwd 430 431 432 rwd rwd rwd 433 434 435 rwd rwd rwd 436 437 438 rwd rwd rwd 439 440 441 rwd rwd rwd 442 443 444 rwd rw rwd 445 446 447 rwd rwd rwd 448 449 450 rwd rwd rwd 451 452 453 rwd rwd rwd 454 455 456 rwd rwd rwd 457 458 459 rwd rwd rwd 460 461 462 ARIMA rwd ARIMA 463 464 465 rwd rwd rwd 466 467 468 rwd ARIMA rwd 469 470 471 ARMA/AR/MA rwd rwd 472 473 474 rwd rwd rwd 475 476 477 rwd ETS-trend rwd 478 479 480 rwd rwd rwd 481 482 483 rwd rwd rwd 484 485 486 rwd rwd rwd 487 488 489 rwd rwd rwd 490 491 492 rwd rwd rwd 493 494 495 rwd rwd theta 496 497 498 rwd theta rwd 499 500 501 rwd rwd rwd 502 503 504 rwd rwd rwd 505 506 507 rwd rwd rwd 508 509 510 rwd rwd rwd 511 512 513 rwd rwd rwd 514 515 516 rwd rwd rwd 517 518 519 ETS-trend rwd rwd 520 521 522 rwd rwd rwd 523 524 525 rwd rwd rwd 526 527 528 rwd rwd rwd 529 530 531 theta rwd rwd 532 533 534 rwd rwd rwd 535 536 537 rwd rwd rwd 538 539 540 rwd rwd rwd 541 542 543 ETS-trend rwd rwd 544 545 546 rwd rwd rwd 547 548 549 rwd rwd rwd 550 551 552 rwd nn rwd 553 554 555 rwd rwd ARIMA 556 557 558 rwd rwd rwd 559 560 561 rwd rwd rwd 562 563 564 rwd ETS-trend rwd 565 566 567 rwd rwd rwd 568 569 570 rwd rwd rwd 571 572 573 rwd rwd theta 574 575 576 rwd rwd rwd 577 578 579 rwd rwd rwd 580 581 582 rwd rwd rwd 583 584 585 rwd rwd rwd 586 587 588 rwd rwd rwd 589 590 591 wn rwd rwd 592 593 594 rwd rwd rwd 595 596 597 theta rwd rwd 598 599 600 rwd rwd rwd 601 602 603 rwd rwd rwd 604 605 606 rwd rwd rwd 607 608 609 rwd rwd rwd 610 611 612 rwd ETS-trend rwd 613 614 615 rwd rwd rwd 616 617 618 ETS-trend ARIMA rwd 619 620 621 rwd ARIMA rwd 622 623 624 rwd rwd rwd 625 626 627 rwd rwd ARIMA 628 629 630 rwd rwd rwd 631 632 633 rwd rwd rwd 634 635 636 rwd rwd wn 637 638 639 wn rwd rwd 640 641 642 rwd nn rwd 643 644 645 wn wn rwd 10 Levels: ARIMA ARMA/AR/MA ETS-dampedtrend ETS-notrendnoseasonal ... wn ``` --- ## seer package: `rf_forecast` ```r predictedlabels_m3 <- rf$predictions forecasts <- rf_forecast(predictions=predictedlabels_m3[1:2], tslist=yearly_m3[1:2], database="M3", function_name="cal_MASE", h=6, accuracy=TRUE) forecasts$mean ``` ``` [,1] [,2] [,3] [,4] [,5] [,6] [1,] 5486.429 6035.865 6585.301 7134.737 7684.173 8233.609 [2,] 4402.227 4574.454 4746.681 4918.908 5091.135 5263.362 ``` --- ## seer package: `rf_forecast` ```r forecasts$lower ``` ``` [,1] [,2] [,3] [,4] [,5] [,6] [1,] 4984.162 4893.098 4629.135 4199.745 3606.858 2848.873 [2,] 2941.377 2430.512 2028.738 1677.572 1355.680 1052.743 ``` ```r forecasts$upper ``` ``` [,1] [,2] [,3] [,4] [,5] [,6] [1,] 5988.696 7178.632 8541.467 10069.729 11761.488 13618.34 [2,] 5863.077 6718.396 7464.623 8160.243 8826.589 9473.98 ``` --- background-image:url(img/m4results.png) background-size: contain --- class: inverse background-image: url(img/forest.jpg) background-size: cover ## Random forest --- class: center, inverse, middle background-image: url(img/forest.jpg) background-size: cover # Can we trust ML-algorithms if we don't know how it works? --- class: inverse background-image: url(img/forest.jpg) background-size: cover ## Peeking inside FFORMS Random forest .full-width[.content-box-yellow[.black[ - **Which** features are the most important? - **Where** are they important? - **How** are they important? - **When and how** are features linked with the prediction outcome? - **When and how strongly** do features interact with other features?]]] --- ## Vote probability matrix .pull-left[ <img class="circle" src="img/newplot.png" width="500px" height="550px"/> ] .pull-right[ <iframe width="690" height="547" src="https://www.youtube.com/embed/XMQRb67gMYQ" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> ] --- class: inverse, middle, center ## .yellow[Which] features are the most important? ## .yellow[Where] are they important? ## .yellow[How] are they important? --- ## Global explanation of feature contribution Overall role of features in the choice of different forecast-model selection. - Permutation-based variable importance - Mean decrease in Gini coefficient - Partial dependence plots (Jerome H. Friedman, 2001) - Individual Conditional Expectation (ICE) curves (Goldstein et al.,2015; Zhao and Hastie, 2017) --- class: inverse, middle, center ##Partial dependence plots and ICE curves --- background-image: url(img/p1.png) background-size: contain --- background-image: url(img/p2.png) background-size: contain --- background-image: url(img/p3.png) background-size: contain --- background-image: url(img/p4.png) background-size: contain --- background-image: url(img/p6.png) background-size: contain --- background-image: url(img/p7.png) background-size: contain --- class: inverse, middle, center ## Feature importance plot for yearly series --- background-image: url(img/y1.png) background-size: contain --- class: inverse, middle, center ## Feature importance plot for quarterly series --- background-image: url(img/q1.png) background-size: contain --- class: inverse, middle, center ## .yellow[When and how] are features linked with the prediction outcome? --- #### Partial dependency plots for quarterly data: strength of seasonality <img src="img/qseasonal.png" width="1703" /> --- ## Partial dependency plots for hourly data: entropy - forecastability of a time series .pull-left[ <img src="img/entropy.png" width="3171" /> ] .pull-right[ <img src="img/en_pdp4.png" width="2620" /> ] --- class: inverse, middle, center ### .yellow[When and how strongly] do features interact with other features? --- ## Interaction effect - Friedman's H-statistic fraction of variance of two-variable partial dependency not captured by sum of the respective individual partial dependencies. --- Interaction between linearity and seasonal lag at seasonally-differenced series <img src="img/htwopdp1-1.png" width="1920" /> --- Interaction between linearity and seasonal lag at seasonally-differenced series <img src="img/htwopdp3-1.png" width="1920" /> --- class: middle, inverse ## Local interpretability --- background-image: url(img/local1.png) background-size: contain --- background-image: url(img/local2.png) background-size: contain --- background-image: url(img/local3.png) background-size: contain --- ## Thank you .pull-left[ <img class="circle" src="img/rob.jpeg" width="250px" height="300px"/> Professor Rob Hyndman Monash University ] .pull-right[ <img class="circle" src="img/george.jpeg" width="200px" height="300px"/> Professor George Athanasopoulos Monash University ] --- class: center, middle # Thank You! <span><i class="fab fa-twitter fa-3x faa-float animated " style=" color:lightblue;"></i></span> <span><i class="fab fa-github fa-3x faa-float animated " style=" color:black;"></i></span> # @thiyangt ### web: https://thiyanga.netlify.app # email: ttalagala@sjp.ac.lk