# tsCV

##### Time series cross-validation

`tsCV`

computes the forecast errors obtained by applying
`forecastfunction`

to subsets of the time series `y`

using a
rolling forecast origin.

- Keywords
- ts

##### Usage

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

##### Arguments

- y
Univariate time series

- forecastfunction
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.- h
Forecast horizon

- window
Length of the rolling window, if NULL, a rolling window will not be used.

- xreg
Exogeneous predictor variables passed to the forecast function if required.

- initial
Initial period of the time series where no cross-validation is performed.

- ...
Other arguments are passed to

`forecastfunction`

.

##### 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.

##### 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.

##### See Also

CV, CVar, residuals.Arima, https://robjhyndman.com/hyndsight/tscv/.

##### Examples

```
# NOT RUN {
#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)
# }
```

*Documentation reproduced from package forecast, version 8.13, License: GPL-3*