What are the main differences apart from the dynamic using lags? I read this paper where the explanation of static factor models was that given N time series of T periods each they can be used to predict of the time series h periods ahead. And I was confused because they only predicted same time period like GDP being predicted by 100 same time variables crammed into 10 variables using PCA. I thought you need a dynamic model to predict h steps ahead as you have trained it for past data to predict future data and the static uses only current time period? Where am I wrong? What are the differences?

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