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If I have a multi-step forecast of some timeseries, where the model is some auto-regressive function

y[t] = f(y[t-1],x1[t],x2[t])

is it a valide approach to use sections of historical data to train the model and than evaluate it on future section recursively to obtain the multi-step forecast. Doing this multiple times with different sections of my historical data I can obtain the forecast error

e[t] = y_hat[t] - y[t]

over the forecast horizon T. Can I use this error to estimate the prediction interval?

Thanks!

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  • $\begingroup$ What are these sections? Why are you doing this? What is the goal? $\endgroup$ – user2974951 Oct 3 '19 at 9:31
  • $\begingroup$ I don't quite understand the question. The sections are sections of 60 days of historical data of the timeseries. I than make a forecast using the data from this section. Then I move the whole section, re-train the predictor and make another forecast. $\endgroup$ – OhmSweetOhm Oct 3 '19 at 18:55
  • $\begingroup$ Are you referring to CV for time series? See robjhyndman.com/hyndsight/tscv $\endgroup$ – user2974951 Oct 4 '19 at 9:51
  • $\begingroup$ Yes but with constant training set length $\endgroup$ – OhmSweetOhm Oct 4 '19 at 20:26
  • $\begingroup$ I don't know why you would do that. Why would you limit your training data like that? $\endgroup$ – user2974951 Oct 7 '19 at 8:07

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