Large-Scale Time Series Forecasting

# Large-Scale Time Series Forecasting
### Thiyanga S. Talagala
### R-Ladies Bergen, Norway
### 24 June 2021

---

## About me

Web: https://thiyanga.netlify.com/

---

---
class: inverse, center, middle
background-image: url(img/jhu.png)
background-position: 50% 60%1

background-size: contain

Let's visualize the coronavirus pandemic!

---
background-image: url(img/coronavirus.png)
background-size: 90px
background-position: 100% 6%

# Data: coronavirus package

```r
install.packages("coronavirus")
# devtools::install_github("RamiKrispin/coronavirus")
```

```r
library(coronavirus)
head(coronavirus, 8)
```

```
        date province             country       lat      long      type cases
1 2020-01-22                  Afghanistan  33.93911  67.70995 confirmed     0
2 2020-01-22                      Albania  41.15330  20.16830 confirmed     0
3 2020-01-22                      Algeria  28.03390   1.65960 confirmed     0
4 2020-01-22                      Andorra  42.50630   1.52180 confirmed     0
5 2020-01-22                       Angola -11.20270  17.87390 confirmed     0
6 2020-01-22          Antigua and Barbuda  17.06080 -61.79640 confirmed     0
7 2020-01-22                    Argentina -38.41610 -63.61670 confirmed     0
8 2020-01-22                      Armenia  40.06910  45.03820 confirmed     0
```

---

<div id="htmlwidget-2e4a23f3bd0bc0b21238" style="width:1080px;height:576px;" class="plotly html-widget"></div>
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104 country: Afghanistan","date: 2020-10-27 cases: 95 country: Afghanistan","date: 2020-10-28 cases: 113 country: Afghanistan","date: 2020-10-29 cases: 123 country: Afghanistan","date: 2020-10-30 cases: 66 country: Afghanistan","date: 2020-10-31 cases: 91 country: Afghanistan","date: 2020-11-01 cases: 76 country: Afghanistan","date: 2020-11-02 cases: 132 country: Afghanistan","date: 2020-11-03 cases: 95 country: Afghanistan","date: 2020-11-04 cases: 86 country: Afghanistan","date: 2020-11-05 cases: 121 country: Afghanistan","date: 2020-11-06 cases: 40 country: Afghanistan","date: 2020-11-07 cases: 58 country: Afghanistan","date: 2020-11-08 cases: 126 country: Afghanistan","date: 2020-11-09 cases: 138 country: Afghanistan","date: 2020-11-10 cases: 166 country: Afghanistan","date: 2020-11-11 cases: 146 country: Afghanistan","date: 2020-11-12 cases: 186 country: Afghanistan","date: 2020-11-13 cases: 174 country: Afghanistan","date: 2020-11-14 cases: 66 country: Afghanistan","date: 2020-11-15 cases: 205 country: Afghanistan","date: 2020-11-16 cases: 228 country: Afghanistan","date: 2020-11-17 cases: 213 country: Afghanistan","date: 2020-11-18 cases: 243 country: Afghanistan","date: 2020-11-19 cases: 253 country: Afghanistan","date: 2020-11-20 cases: 186 country: Afghanistan","date: 2020-11-21 cases: 140 country: Afghanistan","date: 2020-11-22 cases: 203 country: Afghanistan","date: 2020-11-23 cases: 282 country: Afghanistan","date: 2020-11-24 cases: 186 country: Afghanistan","date: 2020-11-25 cases: 210 country: Afghanistan","date: 2020-11-26 cases: 216 country: Afghanistan","date: 2020-11-27 cases: 123 country: Afghanistan","date: 2020-11-28 cases: 121 country: Afghanistan","date: 2020-11-29 cases: 272 country: Afghanistan","date: 2020-11-30 cases: 158 country: Afghanistan","date: 2020-12-01 cases: 242 country: Afghanistan","date: 2020-12-02 cases: 202 country: Afghanistan","date: 2020-12-03 cases: 119 country: Afghanistan","date: 2020-12-04 cases: 0 country: 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2020-09-04 cases: 75 country: Cabo Verde","date: 2020-09-05 cases: 75 country: Cabo Verde","date: 2020-09-06 cases: 55 country: Cabo Verde","date: 2020-09-07 cases: 28 country: Cabo Verde","date: 2020-09-08 cases: 42 country: Cabo Verde","date: 2020-09-09 cases: 73 country: Cabo Verde","date: 2020-09-10 cases: 84 country: Cabo Verde","date: 2020-09-11 cases: 94 country: Cabo Verde","date: 2020-09-12 cases: 60 country: Cabo Verde","date: 2020-09-13 cases: 102 country: Cabo Verde","date: 2020-09-14 cases: 26 country: Cabo Verde","date: 2020-09-15 cases: 65 country: Cabo Verde","date: 2020-09-16 cases: 74 country: Cabo Verde","date: 2020-09-17 cases: 85 country: Cabo Verde","date: 2020-09-18 cases: 78 country: Cabo Verde","date: 2020-09-19 cases: 45 country: Cabo Verde","date: 2020-09-20 cases: 71 country: Cabo Verde","date: 2020-09-21 cases: 24 country: Cabo Verde","date: 2020-09-22 cases: 56 country: Cabo Verde","date: 2020-09-23 cases: 75 country: Cabo Verde","date: 2020-09-24 cases: 67 country: Cabo Verde","date: 2020-09-25 cases: 149 country: Cabo Verde","date: 2020-09-26 cases: 73 country: Cabo Verde","date: 2020-09-27 cases: 70 country: Cabo Verde","date: 2020-09-28 cases: 46 country: Cabo Verde","date: 2020-09-29 cases: 83 country: Cabo Verde","date: 2020-09-30 cases: 124 country: Cabo Verde","date: 2020-10-01 cases: 102 country: Cabo Verde","date: 2020-10-02 cases: 79 country: Cabo Verde","date: 2020-10-03 cases: 91 country: Cabo Verde","date: 2020-10-04 cases: 64 country: Cabo Verde","date: 2020-10-05 cases: 73 country: Cabo Verde","date: 2020-10-06 cases: 85 country: Cabo Verde","date: 2020-10-07 cases: 106 country: Cabo Verde","date: 2020-10-08 cases: 93 country: Cabo Verde","date: 2020-10-09 cases: 92 country: Cabo Verde","date: 2020-10-10 cases: 104 country: Cabo Verde","date: 2020-10-11 cases: 159 country: Cabo Verde","date: 2020-10-12 cases: 83 country: Cabo Verde","date: 2020-10-13 cases: 99 country: Cabo Verde","date: 2020-10-14 cases: 117 country: 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2020-11-24 cases: 98 country: Cabo Verde","date: 2020-11-25 cases: 126 country: Cabo Verde","date: 2020-11-26 cases: 44 country: Cabo Verde","date: 2020-11-27 cases: 56 country: Cabo Verde","date: 2020-11-28 cases: 74 country: Cabo Verde","date: 2020-11-29 cases: 47 country: Cabo Verde","date: 2020-11-30 cases: 14 country: Cabo Verde","date: 2020-12-01 cases: 55 country: Cabo Verde","date: 2020-12-02 cases: 51 country: Cabo Verde","date: 2020-12-03 cases: 71 country: Cabo Verde","date: 2020-12-04 cases: 58 country: Cabo Verde","date: 2020-12-05 cases: 40 country: Cabo Verde","date: 2020-12-06 cases: 27 country: Cabo Verde","date: 2020-12-07 cases: 35 country: Cabo Verde","date: 2020-12-08 cases: 20 country: Cabo Verde","date: 2020-12-09 cases: 74 country: Cabo Verde","date: 2020-12-10 cases: 11 country: Cabo Verde","date: 2020-12-11 cases: 59 country: Cabo Verde","date: 2020-12-12 cases: 40 country: Cabo Verde","date: 2020-12-13 cases: 55 country: Cabo Verde","date: 2020-12-14 cases: 4 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53 country: Cabo Verde","date: 2021-02-14 cases: 41 country: Cabo Verde","date: 2021-02-15 cases: 20 country: Cabo Verde","date: 2021-02-16 cases: 24 country: Cabo Verde","date: 2021-02-17 cases: 63 country: Cabo Verde","date: 2021-02-18 cases: 37 country: Cabo Verde","date: 2021-02-19 cases: 63 country: Cabo Verde","date: 2021-02-20 cases: 51 country: Cabo Verde","date: 2021-02-21 cases: 49 country: Cabo Verde","date: 2021-02-22 cases: 24 country: Cabo Verde","date: 2021-02-23 cases: 17 country: Cabo Verde","date: 2021-02-24 cases: 72 country: Cabo Verde","date: 2021-02-25 cases: 40 country: Cabo Verde","date: 2021-02-26 cases: 52 country: Cabo Verde","date: 2021-02-27 cases: 71 country: Cabo Verde","date: 2021-02-28 cases: 76 country: Cabo Verde","date: 2021-03-01 cases: 32 country: Cabo Verde","date: 2021-03-02 cases: 51 country: Cabo Verde","date: 2021-03-03 cases: 75 country: Cabo Verde","date: 2021-03-04 cases: 63 country: Cabo Verde","date: 2021-03-05 cases: 62 country: Cabo 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Korea, South","date: 2020-10-02 cases: 75 country: Korea, South","date: 2020-10-03 cases: 64 country: Korea, South","date: 2020-10-04 cases: 73 country: Korea, South","date: 2020-10-05 cases: 75 country: Korea, South","date: 2020-10-06 cases: 114 country: Korea, South","date: 2020-10-07 cases: 69 country: Korea, South","date: 2020-10-08 cases: 54 country: Korea, South","date: 2020-10-09 cases: 72 country: Korea, South","date: 2020-10-10 cases: 58 country: Korea, South","date: 2020-10-11 cases: 97 country: Korea, South","date: 2020-10-12 cases: 102 country: Korea, South","date: 2020-10-13 cases: 84 country: Korea, South","date: 2020-10-14 cases: 99 country: Korea, South","date: 2020-10-15 cases: 47 country: Korea, South","date: 2020-10-16 cases: 73 country: Korea, South","date: 2020-10-17 cases: 91 country: Korea, South","date: 2020-10-18 cases: 76 country: Korea, South","date: 2020-10-19 cases: 58 country: Korea, South","date: 2020-10-20 cases: 91 country: Korea, South","date: 2020-10-21 cases: 119 country: Korea, South","date: 2020-10-22 cases: 155 country: Korea, South","date: 2020-10-23 cases: 77 country: Korea, South","date: 2020-10-24 cases: 61 country: Korea, South","date: 2020-10-25 cases: 119 country: Korea, South","date: 2020-10-26 cases: 88 country: Korea, South","date: 2020-10-27 cases: 103 country: Korea, South","date: 2020-10-28 cases: 125 country: Korea, South","date: 2020-10-29 cases: 114 country: Korea, South","date: 2020-10-30 cases: 126 country: Korea, South","date: 2020-10-31 cases: 124 country: Korea, South","date: 2020-11-01 cases: 97 country: Korea, South","date: 2020-11-02 cases: 75 country: Korea, South","date: 2020-11-03 cases: 118 country: Korea, South","date: 2020-11-04 cases: 125 country: Korea, South","date: 2020-11-05 cases: 145 country: Korea, South","date: 2020-11-06 cases: 89 country: Korea, South","date: 2020-11-07 cases: 143 country: Korea, South","date: 2020-11-08 cases: 126 country: Korea, South","date: 2020-11-09 cases: 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2020-11-01 cases: 0 country: Kyrgyzstan","date: 2020-11-02 cases: 1001 country: Kyrgyzstan","date: 2020-11-03 cases: 895 country: Kyrgyzstan","date: 2020-11-04 cases: 535 country: Kyrgyzstan","date: 2020-11-05 cases: 0 country: Kyrgyzstan","date: 2020-11-06 cases: 439 country: Kyrgyzstan","date: 2020-11-07 cases: 556 country: Kyrgyzstan","date: 2020-11-08 cases: 515 country: Kyrgyzstan","date: 2020-11-09 cases: 571 country: Kyrgyzstan","date: 2020-11-10 cases: 970 country: Kyrgyzstan","date: 2020-11-11 cases: 0 country: Kyrgyzstan","date: 2020-11-12 cases: 527 country: Kyrgyzstan","date: 2020-11-13 cases: 567 country: Kyrgyzstan","date: 2020-11-14 cases: 499 country: Kyrgyzstan","date: 2020-11-15 cases: 1030 country: Kyrgyzstan","date: 2020-11-16 cases: 0 country: Kyrgyzstan","date: 2020-11-17 cases: 486 country: Kyrgyzstan","date: 2020-11-18 cases: 425 country: Kyrgyzstan","date: 2020-11-19 cases: 422 country: Kyrgyzstan","date: 2020-11-20 cases: 386 country: Kyrgyzstan","date: 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---

![](index_files/figure-html/unnamed-chunk-5-1.png)

---

![](index_files/figure-html/unnamed-chunk-6-1.png)

---

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background-image: url("img/jhu.png")
background-size: cover

.column.slide-in-left[
.sliderbox.vmiddle.shade_main.center[
.font5[Time Series Features]]]
.column[
]

---

# Time series features

Transform a given time series `$y=\{y_1, y_2, \cdots, y_n\}$` to a feature vector `$F = (f_1(y), f_2(y), \cdots, f_p(y))'$`.

## Examples of time series features

- strength of trend

- strength of seasonality

- lag-1 autocorrelation

- spectral entropy

- proportion of zeros

More information:

Talagala, T. S., Hyndman, R. J., & Athanasopoulos, G. (2018). Meta-learning how to forecast time series. Monash Econometrics and Business Statistics Working Papers, 6, 18.

---

.column.bg-main1[.content.vmiddle.center[

## Time-domain representation

![](index_files/figure-html/unnamed-chunk-7-1.png)

]]

.column.bg-main2[.content.vmiddle.center[

## Feature-domain representation

![](index_files/figure-html/unnamed-chunk-8-1.png)

]]

---

.column.bg-white[.content[

```r
library(tsibble)
norway <- confirmed %>% 
 filter(country == "Norway")
```

]]

.column.bg-white[.content[
]]

---

.column.bg-white[.content[

```r
library(tsibble)
norway <- confirmed %>% 
 filter(country == "Norway")
*norway.tsibble <- tsibble( #
* date = as.Date("2020-01-22") + 0:491, #
* Observation = norway$cases, #
* index = date) #
```

]]

.column.bg-white[.content[
]]

---

.column.bg-white[.content[

```r
library(tsibble)
norway <- confirmed %>% 
 filter(country == "Norway")
norway.tsibble <- tsibble( 
 date = as.Date("2020-01-22") + 0:491, 
 Observation = norway$cases, 
 index = date) 
*norway.tsibble #
```

```
# A tsibble: 492 x 2 [1D]
 date Observation
 <date> <dbl>
 1 2020-01-22 0
 2 2020-01-23 0
 3 2020-01-24 0
 4 2020-01-25 0
 5 2020-01-26 0
 6 2020-01-27 0
 7 2020-01-28 0
 8 2020-01-29 0
 9 2020-01-30 0
10 2020-01-31 0
# … with 482 more rows
```

]]

.column.bg-white[.content[
]]

---

.column.bg-white[.content[

]]

.column.bg-white[.content[

```r
*library(fable) #
*autoplot(norway.tsibble) #
```

![](index_files/figure-html/unnamed-chunk-14-1.png)

]]

---

## Compute features

```r
*library(feasts) #
*norway.tsibble %>% #
* features(Observation, feature_set(tags = #
* c("decomposition", "intermittent", "autocorrelation"))) %>% as.data.frame()#
```

```
  trend_strength seasonal_strength_week seasonal_peak_week seasonal_trough_week
1      0.9158947              0.4880091                  0                    5
  spikiness linearity curvature stl_e_acf1 stl_e_acf10     acf1    acf10
1   5673.13  4291.447  767.7658  -0.206399   0.1942277 0.853502 6.380439
  diff1_acf1 diff1_acf10 diff2_acf1 diff2_acf10 season_acf1     pacf5
1  -0.322936   0.1896912 -0.5713678   0.3516748   0.8460248 0.9376168
  diff1_pacf5 diff2_pacf5 season_pacf zero_run_mean nonzero_squared_cv
1    0.453038    1.107245   0.2593937      6.833333          0.9778515
  zero_start_prop zero_end_prop
1      0.07113821             0
```

---

## tibble

```r
confirmed 
```

```
# A tibble: 94,956 x 3
# Groups: country [193]
 country date cases
 <chr> <date> <dbl>
 1 Afghanistan 2020-01-22 0
 2 Afghanistan 2020-01-23 0
 3 Afghanistan 2020-01-24 0
 4 Afghanistan 2020-01-25 0
 5 Afghanistan 2020-01-26 0
 6 Afghanistan 2020-01-27 0
 7 Afghanistan 2020-01-28 0
 8 Afghanistan 2020-01-29 0
 9 Afghanistan 2020-01-30 0
10 Afghanistan 2020-01-31 0
# … with 94,946 more rows
```

]

## tsibble

```r
confirmed.tsibble <- confirmed %>%
 as_tsibble(index = date, key = country)
confirmed.tsibble
```

```
# A tsibble: 94,956 x 3 [1D]
# Key: country [193]
# Groups: country [193]
 country date cases
 <chr> <date> <dbl>
 1 Afghanistan 2020-01-22 0
 2 Afghanistan 2020-01-23 0
 3 Afghanistan 2020-01-24 0
 4 Afghanistan 2020-01-25 0
 5 Afghanistan 2020-01-26 0
 6 Afghanistan 2020-01-27 0
 7 Afghanistan 2020-01-28 0
 8 Afghanistan 2020-01-29 0
 9 Afghanistan 2020-01-30 0
10 Afghanistan 2020-01-31 0
# … with 94,946 more rows
```

]

---

## Features for all countries

```r
features.all <- confirmed.tsibble %>% features(cases, feature_set(tags = c("decomposition", "intermittent", "autocorrelation")))
features.all
```

```
# A tibble: 193 x 25
 country trend_strength seasonal_strengt… seasonal_peak_we… seasonal_trough…
 <chr> <dbl> <dbl> <dbl> <dbl>
 1 Afghanis… 0.870 0.260 6 5
 2 Albania 0.985 0.493 2 6
 3 Algeria 0.991 0.308 2 4
 4 Andorra 0.684 0.656 6 5
 5 Angola 0.914 0.380 1 6
 6 Antigua … 0.437 0.169 2 5
 7 Argentina 0.980 0.774 2 5
 8 Armenia 0.982 0.876 2 6
 9 Australia 0.833 0.271 1 3
10 Austria 0.984 0.712 2 6
# … with 183 more rows, and 20 more variables: spikiness <dbl>,
# linearity <dbl>, curvature <dbl>, stl_e_acf1 <dbl>, stl_e_acf10 <dbl>,
# acf1 <dbl>, acf10 <dbl>, diff1_acf1 <dbl>, diff1_acf10 <dbl>,
# diff2_acf1 <dbl>, diff2_acf10 <dbl>, season_acf1 <dbl>, pacf5 <dbl>,
# diff1_pacf5 <dbl>, diff2_pacf5 <dbl>, season_pacf <dbl>,
# zero_run_mean <dbl>, nonzero_squared_cv <dbl>, zero_start_prop <dbl>,
# zero_end_prop <dbl>
```

---
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.column.bg-white[.content[

# Feature-based visualization

```r
features.all %>%
  ggplot(aes(x = trend_strength, y =  seasonal_strength_week)) + 
  geom_point() + 
  coord_equal() + 
  xlim(c(0,1)) + ylim(c(0,1)) + 
  labs(x = "Trend strength",
       y = "Seasonal strength") + 
  theme(legend.position = "bottom")
```

]]

.column.bg-white[.content[

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---

# Time-domain

![](index_files/figure-html/unnamed-chunk-21-1.png)

]

# Feature-space

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]

---

class: split-70 hide-slide-number
background-image: url("img/ts.jpeg")
background-size: cover

.column.slide-in-left[
.sliderbox.vmiddle.shade_main.center[
.font5[Large-scale Forecasting]]]
.column[
]

---
class: inverse, center, middle
background-image: url(img/rice1.png)
background-size: contain

# Big picture

---

class: inverse, center, middle
background-image: url(img/rice2.png)
background-size: contain

# Big picture

---
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: Feature-based FORecast Model Selection

### seer (magic ball)

```r
install.packages("seer")
#library(devtools)
#install_github("thiyangt/seer")
library(seer)
```

]

Acropolis Museum, Athens, Greece

]

---

# Example dataset

```r
library(Mcomp)
yearlym1 <- subset(M1, "yearly")
yearlym1
```

```
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
```

---

## Input: features

```r
library(seer)
cal_features(yearlym1[1:2], database="M1",
h=6, highfreq=FALSE)

```

```
# A tibble: 2 x 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 0.00000132 4.46 0.705 -0.0603
2 0.363 0.0790 0.894 0.988 0.989 0.00000154 4.47 0.613 0.272 
# … 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>
```

---

## Output: class labels

```r 
seer::fcast_accuracy(tslist=yearlym1[1:2], 
               models= c("arima","ets","rw", "theta", "nn"), 
               database ="M1", cal_MASE, h=6, 
               length_out = 1, 
               fcast_save = TRUE)
```

```
$accuracy
         arima       ets       rw     theta        nn
YAF2 10.527612 10.319029 13.52428 12.088375 11.811087
YAF3  5.713867  7.704409  7.78949  6.225463  6.700791

$ARIMA
                     YAF2                      YAF3 
"ARIMA(0,1,0) with drift" "ARIMA(0,1,1) with drift"

$ETS
        YAF2         YAF3 
"ETS(A,A,N)" "ETS(M,A,N)"

$forecasts
$forecasts$arima
         YAF2     YAF3
[1,] 579581.0 390955.9
[2,] 605761.9 407325.1
[3,] 631942.9 423694.4
[4,] 658123.8 440063.6
[5,] 684304.8 456432.8
[6,] 710485.7 472802.0

$forecasts$ets
         YAF2     YAF3
[1,] 556280.7 384603.9
[2,] 594333.0 385162.7
[3,] 632385.3 385721.5
[4,] 670437.6 386280.4
[5,] 708489.9 386839.2
[6,] 746542.3 387398.0

$forecasts$rw
       YAF2   YAF3
[1,] 553400 384040
[2,] 553400 384040
[3,] 553400 384040
[4,] 553400 384040
[5,] 553400 384040
[6,] 553400 384040

$forecasts$theta
         YAF2     YAF3
[1,] 565938.8 394342.6
[2,] 578486.4 404640.6
[3,] 591034.0 414938.7
[4,] 603581.5 425236.7
[5,] 616129.1 435534.8
[6,] 628676.6 445832.8

$forecasts$nn
         YAF2     YAF3
[1,] 575410.7 399629.0
[2,] 592457.7 407194.1
[3,] 605225.4 410556.4
[4,] 614538.9 411989.1
[5,] 621198.0 412588.3
[6,] 625889.9 412837.0
```

---

## Training set

```r
prepare_trainingset(accuracy_set = accuracy_m1, 
feature_set = features_m1)$trainingset
```

```
# A tibble: 2 x 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 0.00000132 4.46 0.705 -0.0603
2 0.363 0.0790 0.894 0.988 0.989 0.00000154 4.47 0.613 0.272 
# … with 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>
```

---

## FFORMS classifier

```r
rf <- build_rf(training_set = training_set, 
 testset= M3yearly_features, 
 rf_type="ru", ntree=100, seed=1, 
 import=FALSE, mtry = 8)
```

```r
head(rf$predictions)
```

```
        1         2         3         4         5         6 
ETS-trend       rwd       rwd       rwd       rwd       rwd 
10 Levels: ARIMA ARMA/AR/MA ETS-dampedtrend ETS-notrendnoseasonal ... wn
```

---
class: inverse, center, middle
background-image: url(img/forest.jpg)
background-size: content

---

Source: https://theblue.ai/blog/lime-models-explanation/

---

# explainer package

Machine learning interpretability tools (randomForest)

- 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?

```r
devtools::install_github("thiyangt/explainer")
library(explainer)
```

---
background-image: url(img/ice1.png)
background-size: contain