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I'm doing a rolling forecast using a fitted arma-garch model, but I'm confused regarding the rolling method, my window length is 1209 obs, and I roll 100 times, and each time I reset my window to discard the first obs and add the next obs (thus from 2nd to 1210th in the second rolling window), and everytime I do a one-step-ahead forecast for the next value.

I have 2 questions regarding this process:

  1. I'm not sure whether I should use a dynamic or static forecast(also I read about this definition from the answer here), to be more specific, should I take the forecasted value from last window to form the last value of the next window? Or should I just use the real observation value? And how should I decide this? What's their advantages or disadvantages? My guess is that, it looks like a dynamic one would be more practical in the sense that it requires smaller sample and put more weights on examining the forecasting ability of the model with limited data, while a static one might need more data as everytime it has to take a new real observation, and it is basically a repeated times of examining the model's ability to do a one-step-ahead forecast. (Also I'm not sure if my logic is right or not due to my lack of profound understanding of the models, so pls point out if I'm wrong:))

  2. This is a question regarding the concept of in-sample and out-of-sample. I separate my sample into in-sample(first 1209 obs) and out-of-sample dataset(the rest 100 obs), and I use the in-sample data to estimate a model and use a window length of 1209 to do one-step-ahead forecast, in the case of static forecast, then everytime I have to take the new obs, for example, the first time I take first 1st to 1209th obs to forecast for the 1210th one, and the second window I use the 2nd to 1210th obs to forecast for the 1211th one, in this case, can I still call my out-of-sample data "out-of-sample"? As it also contributes to form the new window every time, thus it is no longer "out-of-sample" ?

Many thanks for the help!

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  1. What you should do depends on what you are interested in. If you want to assess how well your model predicts one step ahead, then use static one-step-ahead forecasts. If you are interested in how well your model predicts $h$ steps ahead (where $h>1$), use static $h$-step-ahead forecasts. If you want to see paths of 1 to $h$-step-ahead forecasts, do dynamic $h$-step-ahead forecasting and look at the trajectories across the rolling windows.
  2. You got the scheme of things right, but no worries, these are proper out-of-sample forecasts. It is just that in a rolling window setting, the "out sample" gradually becomes the "in sample". But it does in no way contaminate the results or make them unfair: each time you are forecasting a data point that was not used in building and estimating the model, so each time you are forecasting out of sample.
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