tsCV computes the forecast errors obtained by applying forecastfunction to subsets of the time series y using a rolling forecast origin.

tsCV(y, forecastfunction, h = 1, window = NULL, xreg = NULL, initial = 0, ...)

## Arguments

y Univariate time series Function to return an object of class forecast. Its first argument must be a univariate time series, and it must have an argument h for the forecast horizon. Forecast horizon Length of the rolling window, if NULL, a rolling window will not be used. Exogeneous predictor variables passed to the forecast function if required. Initial period of the time series where no cross-validation is performed. Other arguments are passed to forecastfunction.

## Value

Numerical time series object containing the forecast errors as a vector (if h=1) and a matrix otherwise. The time index corresponds to the last period of the training data. The columns correspond to the forecast horizons.

## Details

Let y contain the time series $$y_1,\dots,y_T$$. Then forecastfunction is applied successively to the time series $$y_1,\dots,y_t$$, for $$t=1,\dots,T-h$$, making predictions $$\hat{y}_{t+h|t}$$. The errors are given by $$e_{t+h} = y_{t+h}-\hat{y}_{t+h|t}$$. If h=1, these are returned as a vector, $$e_1,\dots,e_T$$. For h>1, they are returned as a matrix with the hth column containing errors for forecast horizon h. The first few errors may be missing as it may not be possible to apply forecastfunction to very short time series.

Rob J Hyndman

## Examples


#Fit an AR(2) model to each rolling origin subset
far2 <- function(x, h){forecast(Arima(x, order=c(2,0,0)), h=h)}
e <- tsCV(lynx, far2, h=1)

#Fit the same model with a rolling window of length 30
e <- tsCV(lynx, far2, h=1, window=30)