Why do simple time series models sometimes outperform regression models fitted to nonstationary data?
• Two nonstationary time series X and Y generally don’t stay perfectly “in synch” over long periods of time–i.e., they do not usually maintain a perfectly linear relationship–even if they are causally related. • There may be some “omitted variable”, say Z, which could in principle explain some of the discrepancy in the relationship between X and Y–but this is not the only possibility. For example, the nature of the relationship between X and Y may simply change over time. Remember that if X and Y are nonstationary, this means that we cannot necessarily assume their statistical properties (such as their correlations with each other) are constant over time. • If the variables X and Z change relatively slowly from period to period, it is possible that the information X(t) and Z(t) contain with respect to Y(t) is already contained in Y(t-1), Y(t-2), etc.–i.e., in Y’s own recent history–which time series models are able to utilize. In other words, recent values of Y might be good “prox
