This question is addressed to expert in econometrics. I generally fit econometric models and statistical learning models to financial time series and some discretionary traders usually asked me if I try to "catch momentum or mean-reversion" and I always reply to them "both". Am I right?
Using the best fit, for instance using AIC to select a vector ARMA, I should be able to capture the dynamic of the financial time series both auto correlation and causality/cross-correlation. Depending on the input I could have a forecast telling me the prices are trending or mean-reverting.
I realised though that the vector ARMA can rarely catch both effect at the same time. For instance an AR(1) the simplest model is always a mean-reverting model (if stationary). An integrated AR(1) (ARIMA(1,1,0)) is always a momentum model, as the change of prices will converge to the mean change of price (if the mean is positive and the mean is large compare to the standard deviation, this is a momentum model). Can more complex models Vector ARMA achieve to catch both dynamic? Or is it always one or the other?