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I have a time-series that I am trying to fit an autoregression model to. I am trying to use the tsCV method. From the help page I find this:

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

and from the details section I see

Let y contain the time series y[1:T]. Then forecastfunction is applied successively to the time series y[1:t], for t=1,…,T-h, making predictions f[t+h].

In the examples we have

far2 <- function(x, h){forecast(Arima(x, order=c(2,0,0)), h=h)}
e <- tsCV(lynx, far2, h=1)

meaning that forecast(Arima(x,order=c(2,0,0)),h=h) would be applied successively to the time series lynx using the rolling forecast origin. To make this only slightly more complicated, there is also the window argument which provides a rolling window instead of a rolling origin. My question is: when we apply forecast(Arima(x,order=c(2,0,0)),h=h) repeatedly are we repeatedly training a new ARIMA model on the new window of the time-series data? Or, is there some how and somewhere a persistent ARIMA model that is trained only once and then referenced for the further calls of the forecast method?

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It is repeatedly training a new ARIMA model on each subset of data.

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