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I'm using the ets forecast function in R.

When I fit a model to some timeseries t1:

   model<-ets(t1) [36 periods]

and the calculate forecasts from that model:

    f1 <- forecast(model,10)

so i get 10 forecasts for periods 37-48

so my question is, are these 10 point-forecast one-step-ahead forecasts wich have their seeds in $t,t+1,t+2$ with $t=37$

or are these forecasts with their seed only in $t=37$ with forecast horizon $h=1,2,3,4,...$

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  • $\begingroup$ Thx for the quick reply, if i have understand it right the one-step forecasts are then provided by splitting a time series in two sequences: [60 Periods] t1<-[36 periods] fitting sample t2<-[24 periods] test sample.....both tseries objects. fit the model within the first periods: model1<-ets(t1) then using the model to the out-of-sample data t2: test<-ets(t2,model=model1) and the one-step-ahead forecast with seeds in t=37,38 is preserved by fitted(test). am i right? or how can i get the one-step forecasts to an test data-set using the model i estimated from a fitting data-set. thx in advance T $\endgroup$ – user4667 May 19 '11 at 11:45
  • $\begingroup$ Yes, that would give the one-step forecasts in the test set. ets() does not try to guess the seasonality. If you don't include the frequency, you will only get non-seasonal models. $\endgroup$ – Rob Hyndman May 19 '11 at 23:42
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They can't possibly be one-step forecasts because you haven't provided any data for t>36. They are forecasts of times 37,...,46 based on data up to time 36 (i.e., horizons 1,2,3,...,10).

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A point of clarification but in my opinion all ARIMA forecasts are "one-step ahead forecasts". In the "fitting area t<37" the fitted values are 1 period/step ahead forecasts. In the absence of data beyond t>36 the procedure is to use the PREDICTED VALUE as if it were the ACTUAL VALUE thus bootstrapping the forecast. For example the forecast for period 38 will be a one-step ahead forecast as it will assume that the predicted value for period 37 is the "actual" for period 37. This is precisely why forecast accuracy measured from a single origin is tainted because the forecasts are correlated as they are obtained from a recursive scheme. If a one period out forecast is "wrong" then subsequent "wrong forecasts" may ensue. One is always better off by looking at forecast accuracies from a number of origins in order to assess model performance.

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