The seer package provides implementations of a novel framework for forecast model selection using time series features. We call this framework FFORMS (Feature-based FORecast Model Selection). For more details see our paper.

Installation

You can install seer from github with:

Usage

The FFORMS framework consists of two main phases: i) offline phase, which includes the development of a classification model and ii) online phase, use the classification model developed in the offline phase to identify “best” forecast-model. This document explains the main functions using a simple dataset based on M3-competition data. To load data,

FFORMS: offline phase

1. Augmenting the observed sample with simulated time series.

We augment our reference set of time series by simulating new time series. In order to produce simulated series, we use several standard automatic forecasting algorithms such as ETS or automatic ARIMA models, and then simulate multiple time series from the selected model within each model class. sim_arimabased can be used to simulate time series based on (S)ARIMA models.

Similarly, sim_etsbased can be used to simulate time series based on ETS models.

simulated_ets <- lapply(m3y, sim_etsbased, Future=TRUE, Nsim=2, extralength=6, Combine=FALSE)
simulated_ets

2. Calculate features based on the training period of time series.

Our proposed framework operates on the features of the time series. cal_features function can be used to calculate relevant features for a given list of time series.

Calculate features from the simulated time series in the step 1

3. Calculate forecast accuracy measure(s)

fcast_accuracy function can be used to calculate forecast error measure (in the following example MASE) from each candidate model. This step is the most computationally intensive and time-consuming, as each candidate model has to be estimated on each series. In the following example ARIMA(arima), ETS(ets), random walk(rw), random walk with drift(rwd), standard theta method(theta) and neural network time series forecasts(nn) are used as possible models. In addition to these models following models can also be used in the case of handling seasonal time series,

  • snaive: seasonal naive method
  • stlar: STL decomposition is applied to the time series and then seasonal naive method is used to forecast seasonal component. AR model is used to forecast seasonally adjusted data.
  • mstlets: STL decomposition is applied to the time series and then seasonal naive method is used to forecast seasonal component. ETS model is used to forecast seasonally adjusted data.
  • mstlarima: STL decomposition is applied to the time series and then seasonal naive method is used to forecast seasonal component. ARIMA model is used to forecast seasonally adjusted data.
  • tbats: TBATS models
tslist <- list(M3[[1]], M3[[2]])
accuracy_info <- fcast_accuracy(tslist=tslist, models= c("arima","ets","rw","rwd", "theta", "nn"), database ="M3", cal_MASE, h=6, length_out = 1, fcast_save = TRUE)
accuracy_info
#> $accuracy
#>         arima       ets       rw       rwd    theta        nn
#> [1,] 1.566974 1.5636089 7.703518 4.2035176 6.017236 2.5408796
#> [2,] 1.698388 0.9229687 1.698388 0.6123443 1.096000 0.2797441
#> 
#> $ARIMA
#> [1] "ARIMA(0,2,0)" "ARIMA(0,1,0)"
#> 
#> $ETS
#> [1] "ETS(M,A,N)" "ETS(M,A,N)"
#> 
#> $forecasts
#> $forecasts$arima
#>         [,1] [,2]
#> [1,] 5486.10 4230
#> [2,] 6035.21 4230
#> [3,] 6584.32 4230
#> [4,] 7133.43 4230
#> [5,] 7682.54 4230
#> [6,] 8231.65 4230
#> 
#> $forecasts$ets
#>          [,1]     [,2]
#> [1,] 5486.429 4347.678
#> [2,] 6035.865 4465.365
#> [3,] 6585.301 4583.052
#> [4,] 7134.737 4700.738
#> [5,] 7684.173 4818.425
#> [6,] 8233.609 4936.112
#> 
#> $forecasts$rw
#>         [,1] [,2]
#> [1,] 4936.99 4230
#> [2,] 4936.99 4230
#> [3,] 4936.99 4230
#> [4,] 4936.99 4230
#> [5,] 4936.99 4230
#> [6,] 4936.99 4230
#> 
#> $forecasts$rwd
#>         [,1]     [,2]
#> [1,] 5244.40 4402.227
#> [2,] 5551.81 4574.454
#> [3,] 5859.22 4746.681
#> [4,] 6166.63 4918.908
#> [5,] 6474.04 5091.135
#> [6,] 6781.45 5263.362
#> 
#> $forecasts$theta
#>         [,1]     [,2]
#> [1,] 5085.07 4321.416
#> [2,] 5233.19 4412.843
#> [3,] 5381.31 4504.269
#> [4,] 5529.43 4595.696
#> [5,] 5677.55 4687.122
#> [6,] 5825.67 4778.549
#> 
#> $forecasts$nn
#>          [,1]     [,2]
#> [1,] 5508.025 4791.397
#> [2,] 6056.273 5061.414
#> [3,] 6527.626 5151.932
#> [4,] 6887.316 5177.717
#> [5,] 7133.450 5184.683
#> [6,] 7288.078 5186.538

4. Construct a dataframe of input:features and output:lables to train a random forest

prepare_trainingset can be used to create a data frame of input:features and output: labels.

# steps 3 and 4 applied to yearly series of M1 competition
data(M1)
yearly_m1 <- subset(M1, "yearly")
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)
features_m1 <- cal_features(yearly_m1, database="M1", h=6, highfreq = FALSE)

# prepare training set
prep_tset <- prepare_trainingset(accuracy_set = accuracy_m1, feature_set = features_m1)

# provides the training set to build a rf classifier
head(prep_tset$trainingset)
#> # A tibble: 6 x 26
#>   entropy lumpiness stability hurst trend spikiness linearity curvature
#>     <dbl>     <dbl>     <dbl> <dbl> <dbl>     <dbl>     <dbl>     <dbl>
#> 1   0.683   0.0400      0.977 0.985 0.985   1.32e-6      4.46    0.705 
#> 2   0.711   0.0790      0.894 0.988 0.989   1.54e-6      4.47    0.613 
#> 3   0.716   0.0160      0.858 0.987 0.989   1.13e-6      4.60    0.695 
#> 4   0.761   0.00201     1.32  0.982 0.957   8.96e-6      4.48    0.0735
#> 5   0.628   0.00112     0.446 0.993 0.973   1.80e-6      5.77    1.21  
#> 6   0.708   0.00774     0.578 0.986 0.975   3.31e-6      4.75    0.748 
#> # … with 18 more variables: e_acf1 <dbl>, 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>

# provides additional information about the fitted models
head(prep_tset$modelinfo)
#> # A tibble: 6 x 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)

FFORMS: online phase is activated.

5. Train a random forest and predict class labels for new series (FFORMS: online phase)

build_rf in the seer package enables the training of a random forest model and predict class labels (“best” forecast-model) for new time series. In the following example we use only yearly series of the M1 and M3 competitions to illustrate the code. A random forest classifier is build based on the yearly series on M1 data and predicted class labels for yearly series in the M3 competition. Users can further add the features and classlabel information calculated based on the simulated time series.

6. Generate point foecasts and 95% prediction intervals

rf_forecast function can be used to generate point forecasts and 95% prediction intervals based on the predicted class labels obtained in step

Notes

Calculation of features for daily series

# install.packages("https://github.com/carlanetto/M4comp2018/releases/download/0.2.0/M4comp2018_0.2.0.tar.gz",
#                 repos=NULL)
library(M4comp2018)
data(M4)
# extract first two daily time series
M4_daily <- Filter(function(l) l$period == "Daily", M4)
# convert daily series into msts objects
M4_daily_msts <- lapply(M4_daily, function(temp){
  temp$x <- convert_msts(temp$x, "daily")
  return(temp)
})
# calculate features
seer::cal_features(M4_daily_msts, seasonal=TRUE, h=14, m=7, lagmax=8L, database="M4", highfreq=TRUE)
#> # A tibble: 4,227 x 26
#>    entropy lumpiness stability hurst trend spikiness linearity curvature
#>      <dbl>     <dbl>     <dbl> <dbl> <dbl>     <dbl>     <dbl>     <dbl>
#>  1   0.327   0.00214     0.621 1.000 0.993  1.09e-10     31.1      3.09 
#>  2   0.369   0.331       0.446 1.000 0.865  2.53e- 8     24.7      1.35 
#>  3   0.659   0.755       0.761 0.999 0.917  4.49e- 6      3.82     4.89 
#>  4   0.819   0.168       0.821 0.996 0.841  3.86e- 6      1.87     6.38 
#>  5   0.512   0.0140      0.991 1.000 0.988  4.64e- 8     11.3      0.878
#>  6   0.328   0.00136     0.242 1.000 0.989  1.90e-10     29.8      8.27 
#>  7   0.498   0.247       0.697 0.999 0.845  2.38e- 8     24.1      1.96 
#>  8   0.365   0.0189      1.01  1.000 0.968  2.31e- 9     30.1     -4.98 
#>  9   0.384   0.0275      1.07  1.000 0.954  4.69e- 9     29.3     -6.67 
#> 10   0.509   0.00110     0.974 1.000 0.989  8.77e-10     18.3     -3.60 
#> # … with 4,217 more rows, and 18 more variables: e_acf1 <dbl>,
#> #   y_acf1 <dbl>, diff1y_acf1 <dbl>, diff2y_acf1 <dbl>, y_pacf5 <dbl>,
#> #   diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, nonlinearity <dbl>,
#> #   seas_pacf <dbl>, seasonal_strength1 <dbl>, seasonal_strength2 <dbl>,
#> #   sediff_acf1 <dbl>, sediff_seacf1 <dbl>, sediff_acf5 <dbl>, N <int>,
#> #   y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl>

Calculation of features for hourly series