correct AR model and cross sectional data

Does every AR model has serial correlation problem? do we need to add lag to correct the auto-correlation problem ? in macroeconomic multifactor model, is it time series or cross sectional data? in macroeconomic model, we didn’t compare with peers like fundamental model, so it is not cross sectional, am I right?

any idea? thanks

I don’t think that you can have an AR model if there isn’t some kind of serial correlation in the data. The whole point of AR or MA is to use the fact that there is serial correlation to try to predict the next point in the series. Macroeconomic factor models are most likely panel data that are treated as cross section. That is, there is a time dimension and there is an asset dimension (you estimate different betas for each asset) but in general the time dimension is pooled and treated as if it were cross sectional data. Macroeconomic factor models could potentially incorporate a time series element, such as a momentum factor in GDP or inflation or whatever, but I doubt they would throw that level of complexity at you, so you can treat these as if they are pooled longitudinal data rather than do the full time-series approach.