# Which one should I use for rolling forecast, dynamic or static?

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!

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.