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.
You could install the stable version on CRAN:
You could install the development version from Github using
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,
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.
library(seer)
simulated_arima <- lapply(m3y, sim_arimabased, Future=TRUE, Nsim=2, extralength=6, Combine=FALSE)
simulated_arima
#> $N0001
#> $N0001[[1]]
#> Time Series:
#> Start = 1989
#> End = 2008
#> Frequency = 1
#> [1] 5570.194 6175.587 6737.455 7172.934 7692.446 8260.463 8862.822
#> [8] 9318.833 9754.845 10173.877 10503.480 10731.675 11034.088 11446.391
#> [15] 11774.318 12166.994 12640.379 13234.508 13870.481 14364.186
#>
#> $N0001[[2]]
#> Time Series:
#> Start = 1989
#> End = 2008
#> Frequency = 1
#> [1] 5378.075 5795.233 6268.063 6845.178 7209.492 7489.012 7771.217 8181.615
#> [9] 8599.027 8854.889 9163.976 9452.008 9535.338 9496.047 9492.168 9429.858
#> [17] 9235.976 8975.386 8757.015 8395.180
#>
#>
#> $N0002
#> $N0002[[1]]
#> Time Series:
#> Start = 1989
#> End = 2008
#> Frequency = 1
#> [1] 4869.718 4091.624 4202.994 3993.931 4470.837 4359.409 5300.641 5311.870
#> [9] 5259.591 4919.559 6189.519 5860.118 4953.813 5102.404 4869.983 3485.111
#> [17] 4085.780 4207.551 3938.959 5472.136
#>
#> $N0002[[2]]
#> Time Series:
#> Start = 1989
#> End = 2008
#> Frequency = 1
#> [1] 5187.0120 5877.9544 5125.4700 4904.6038 3979.0852 4805.9765 5853.8952
#> [8] 5236.6049 5320.8282 4410.9000 3638.2943 3510.4286 3896.0295 2977.3216
#> [15] 1901.7726 1503.2627 1397.3442 1514.6785 995.8874 894.7566Similarly, 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_ets2. 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.
library(tsfeatures)
M3yearly_features <- seer::cal_features(yearly_m3, database="M3", h=6, highfreq = FALSE)
head(M3yearly_features)
#> # A tibble: 6 x 25
#> entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.773 0 0 0.971 0.995 2.37e-7 3.58 0.424 0.412
#> 2 0.837 0 0 0.947 0.869 1.79e-4 2.05 -2.08 0.324
#> 3 0.825 0 0 0.949 0.865 1.93e-4 1.75 -2.26 0.457
#> 4 0.854 0 0 0.949 0.853 3.68e-4 2.87 -1.25 0.281
#> 5 0.899 0 0 0.855 0.586 1.27e-3 -0.765 -1.77 0.192
#> 6 0.798 0 0 0.964 0.964 2.17e-5 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>Calculate features from the simulated time series in the step 1
features_simulated_arima <- lapply(simulated_arima, function(temp){
lapply(temp, cal_features, h=6, database="other", highfreq=FALSE)})
fea_sim <- lapply(features_simulated_arima, function(temp){do.call(rbind, temp)})
do.call(rbind, fea_sim)
#> # A tibble: 4 x 25
#> entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
#> * <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.768 0 0 0.973 0.999 3.13e-9 3.56 -0.322 0.439
#> 2 0.774 0 0 0.973 0.996 1.99e-7 3.55 -0.454 0.216
#> 3 0.924 0 0 0.857 0.606 1.14e-3 2.09 -0.153 0.0178
#> 4 0.918 0 0 0.895 0.679 1.11e-3 -2.41 -1.08 0.175
#> # … 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>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,
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 2.5817848
#> [2,] 1.698388 0.9229687 1.698388 0.6123443 1.096000 0.2797567
#>
#> $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,] 5508.903 4791.327
#> [2,] 6055.437 5061.321
#> [3,] 6521.419 5151.862
#> [4,] 6872.999 5177.666
#> [5,] 7110.509 5184.642
#> [6,] 7257.809 5186.5004. 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$trainingset)
#> # A tibble: 6 x 26
#> entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.683 0.0400 0.977 0.985 0.985 1.32e-6 4.46 0.705 -0.0603
#> 2 0.711 0.0790 0.894 0.988 0.989 1.54e-6 4.47 0.613 0.272
#> 3 0.716 0.0160 0.858 0.987 0.989 1.13e-6 4.60 0.695 0.172
#> 4 0.761 0.00201 1.32 0.982 0.957 8.96e-6 4.48 0.0735 -0.396
#> 5 0.628 0.00112 0.446 0.993 0.973 1.80e-6 5.77 1.21 0.0113
#> 6 0.708 0.00774 0.578 0.986 0.975 3.31e-6 4.75 0.748 -0.385
#> # … with 17 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, diff2y_acf1 <dbl>,
#> # y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, nonlinearity <dbl>,
#> # lmres_acf1 <dbl>, ur_pp <dbl>, ur_kpss <dbl>, N <int>, y_acf5 <dbl>,
#> # diff1y_acf5 <dbl>, diff2y_acf5 <dbl>, alpha <dbl>, beta <dbl>,
#> # classlabels <chr>
# provides additional information about the fitted models
head(prep_tset$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)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.
rf <- build_rf(training_set = prep_tset$trainingset, testset=M3yearly_features, rf_type="rcp", ntree=100, seed=1, import=FALSE, mtry = 8)
#> Warning in if (testset == FALSE) {: the condition has length > 1 and only the
#> first element will be used
# to get the predicted class labels
predictedlabels_m3 <- rf$predictions
table(predictedlabels_m3)
#> predictedlabels_m3
#> ARIMA ARMA/AR/MA ETS-dampedtrend
#> 63 0 0
#> ETS-notrendnoseasonal ETS-trend nn
#> 4 26 15
#> rw rwd theta
#> 2 527 3
#> wn
#> 5
# to obtain the random forest for future use
randomforest <- rf$randomforest6. Generate point foecasts and 95% prediction intervals
rf_forecast function can be used to generate point forecasts and 95% prediction intervals based on the predicted class labels obtained in step 5.
forecasts <- rf_forecast(predictions=predictedlabels_m3[1:2], tslist=yearly_m3[1:2], database="M3", function_name="cal_MASE", h=6, accuracy=TRUE)
# to obtain point forecasts
forecasts$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
# to obtain lower boundary of 95% prediction intervals
forecasts$lower
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 4984.162 4893.098 4629.135 4199.745 3606.858 2848.873
#> [2,] 2941.377 2430.512 2028.738 1677.572 1355.680 1052.743
# to obtain upper boundary of 95% prediction intervals
forecasts$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
# to obtain MASE
forecasts$accuracy
#> [1] 1.5636089 0.6123443Calculation of features for daily series
# install.packages("https://github.com/carlanetto/M4comp2018/releases/download/0.2.0/M4comp2018_0.2.0.tar.gz",
# repos=NULL)
library(M4comp2018)
data(M4)
# extract first two daily time series
M4_daily <- Filter(function(l) l$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 e_acf1
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.327 0.00214 0.621 1.00 0.993 1.09e-10 31.1 3.09 0.976
#> 2 0.369 0.331 0.446 1.00 0.865 2.53e- 8 24.7 1.35 0.986
#> 3 0.659 0.755 0.761 0.999 0.917 4.49e- 6 3.82 4.89 0.318
#> 4 0.819 0.168 0.821 0.996 0.841 3.86e- 6 1.87 6.38 0.290
#> 5 0.512 0.0140 0.991 1.00 0.988 4.64e- 8 11.3 0.878 0.376
#> 6 0.328 0.00136 0.242 1.00 0.989 1.90e-10 29.8 8.27 0.973
#> 7 0.498 0.247 0.697 0.999 0.845 2.38e- 8 24.1 1.96 0.809
#> 8 0.365 0.0189 1.01 1.00 0.968 2.31e- 9 30.1 -4.98 0.963
#> 9 0.384 0.0275 1.07 1.00 0.954 4.69e- 9 29.3 -6.67 0.963
#> 10 0.509 0.00110 0.974 1.00 0.989 8.77e-10 18.3 -3.60 0.346
#> # … with 4,217 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>, 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
data(M4)
# extract first two daily time series
M4_hourly <- Filter(function(l) l$period == "Hourly", M4)[1:2]
## convert data into msts object
hourlym4_msts <- lapply(M4_hourly, function(temp){
temp$x <- convert_msts(temp$x, "hourly")
return(temp)
})
cal_features(hourlym4_msts, seasonal=TRUE, m=24, lagmax=25L,
database="M4", highfreq = TRUE)
#> Warning: Unknown columns: `seasonal_strength`
#> # A tibble: 2 x 26
#> entropy lumpiness stability hurst trend spikiness linearity curvature e_acf1
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.524 0.0110 0.0899 0.999 0.626 1.92e-8 5.33 -3.51 0.958
#> 2 0.540 0.0505 0.109 0.999 0.790 6.39e-9 7.85 -0.152 0.974
#> # … with 17 more variables: y_acf1 <dbl>, diff1y_acf1 <dbl>, diff2y_acf1 <dbl>,
#> # y_pacf5 <dbl>, diff1y_pacf5 <dbl>, diff2y_pacf5 <dbl>, nonlinearity <dbl>,
#> # seas_pacf <dbl>, seasonal_strength1 <dbl>, seasonal_strength2 <dbl>,
#> # sediff_acf1 <dbl>, sediff_seacf1 <dbl>, sediff_acf5 <dbl>, N <int>,
#> # y_acf5 <dbl>, diff1y_acf5 <dbl>, diff2y_acf5 <dbl># extract only the values for two time series just for illustration
yearly_m1_features <- features_m1[1:2,]
votes.matrix <- predict(rf$randomforest, yearly_m1_features, type="vote")
tslist <- yearly_m1[1:2]
# To identify models and weights for forecast combination
models_and_weights_for_combinations <- fforms_ensemble(votes.matrix, threshold=0.6)
# Compute combination forecast
fforms_combinationforecast(models_and_weights_for_combinations, tslist, "M1", 6)
#> [[1]]
#> [[1]]$mean
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 556280.7 594333 632385.3 670437.6 708489.9 746542.3
#>
#> [[1]]$lower
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 495633.6 530117.6 561088.8 588269.7 611931.4 632551.3
#>
#> [[1]]$upper
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 616927.8 658548.4 703681.8 752605.5 805048.5 860533.2
#>
#>
#> [[2]]
#> [[2]]$mean
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 400921.2 417802.4 434683.5 451564.7 468445.9 485327.1
#>
#> [[2]]$lower
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 357623.1 355193.4 356354.4 359252.9 363194.2 367833.3
#>
#> [[2]]$upper
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 444219.3 480411.3 513012.7 543876.6 573697.6 602820.9