We consider linear predictor definitions of noncausality or strict exogeneity and show that it is restrictive to assert that there exists a time-invariant latent variable c such that x is strictly exogenous conditional on c. A restriction of this sort is necessary to justify standard techniques...

Under stationarity, the heterogeneous stoahastic processes are the non-ergodic ones. We show that if a distributed lag is of finite order, then its coefficients are unconditional means of the underlying random coefficients. This result is applied to linear transformations of the process. The...