In thiyangt/seer: Feature-Based Forecast Model Selection

seer

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "README-"
)

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 could install the stable version on CRAN:

install.packages("seer")

You could install the development version from Github using

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

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,

library(Mcomp)
data(M3)
yearly_m3 <- subset(M3, "yearly")
m3y <- M3[1:2]

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.

library(seer)
simulated_arima <- lapply(m3y, sim_arimabased, Future=TRUE, Nsim=2, extralength=6, Combine=FALSE)
simulated_arima

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.

library(tsfeatures)
M3yearly_features <- seer::cal_features(yearly_m3, database="M3", h=6, highfreq = FALSE)
head(M3yearly_features)

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)

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

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)

# provides additional information about the fitted models
head(prep_tset$modelinfo)

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.

rf <- build_rf(training_set = prep_tset$trainingset, testset=M3yearly_features,  rf_type="rcp", ntree=100, seed=1, import=FALSE, mtry = 8)

# to get the predicted class labels
predictedlabels_m3 <- rf$predictions
table(predictedlabels_m3)

# to obtain the random forest for future use
randomforest <- rf$randomforest

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 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

# to obtain lower boundary of 95% prediction intervals
forecasts$lower

# to obtain upper boundary of 95% prediction intervals
forecasts$upper

# to obtain MASE
forecasts$accuracy

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)

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)

Forecast combinations based on FFORMS algorithm

# 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)