What are the default train and test set sizes for the forecast() function in R?

Question

I have used the TBATS model on my data and when I apply the forecast() function, it automatically forecasts two years in the future. I haven't specified any training set or testing set, so how do I know how much data it used to predict the next two years?

The data I'm dealing with is Uber travel times data from Jan 2016 to Jan 2020. I have daily data (sampling frequency = 1) for 18 cities and each city has a different sample size (they range from 1422 days to 1459 days).

I have set the vector of travel times as an msts object, for it has multiple seasonality, which is used by the TBATS model.

When I calculate RMSE, MAE, MAPE and MSE, I get very low values in general, so how can I know which data TBATS is training on?

Here is my code:

data <- read.csv('C:/users/Datasets/Final Datasets/final_a.csv', TRUE, ",")
y <- msts(data$MeanTravelTimeSeconds, start=c(2016,1), seasonal.periods=c(7.009615384615385, 30.5, 91.3, 365.25))

fit <- tbats(y)
plot(fit)
fc <- forecast(fit)
autoplot(fc, ylab = "Travel Time in Seconds")

# Check residuals (ACF and histogram)
checkresiduals(fc)

# RMSE
rmse <- sqrt(fit$variance)

# MAE
res <- residuals(fit)
mae <- mean(abs(res))

# MAPE
pt <- (res)/y
mape <- mean(abs(pt))

# MSE (Mean Squared Error)
mse <- mean(res^2)

The performance results for the TBATS model for Amsterdam are:

RMSE: 0.06056063
MAE: 0.04592825
MAPE: 6.474616e-05
MSE: 0.00366759

If I had to manually select the test and train sets, how should I modify my code in order to do so?

Answer 1

If you use forecast(fit), as you did, what you get is the fitted vales from the training data.

If you want to use a test set as well see below for an example. You use the fitted model to forecast to a horizon h and compare with known data set.

library(forecast)

# Training Data
n_train <- round(length(USAccDeaths) * 0.8)
train <- head(USAccDeaths, n_train)

# Test Data
n_test <- length(USAccDeaths) - n_train
test <- tail(USAccDeaths, n_test)

# Model Fit
fit <- tbats(train)

# Forecast for the same horizion as the test data
fc <- forecast(fit, n_test)

# Point Forecasts 
fc$mean
#            Jan       Feb       Mar       Apr       May       Jun       Jul
# 1977                      7767.513  7943.791  8777.425  9358.863 10034.996
# 1978  7711.478  7004.621  7767.513  7943.791  8777.425  9358.863 10034.996
#            Aug       Sep       Oct       Nov       Dec
# 1977  9517.860  8370.509  8706.441  8190.262  8320.606
# 1978  9517.860  8370.509  8706.441  8190.262  8320.606

test # for comparison with the point forecasts
#        Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
# 1977              7726  8106  8890  9299 10625  9302  8314  8850  8265  8796
# 1978  7836  6892  7791  8192  9115  9434 10484  9827  9110  9070  8633  9240

It would be interesting to see how plots like the following would behave as well.

autoplot(USAccDeaths) + autolayer(fc) + autolayer(fitted(fit))
#autoplot(USAccDeaths) +  autolayer(fitted(fit))