Strong Laws of Large Numbers for Dependent Heterogeneous Processes: a Synthesis of Recent and Newresults

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a strong law for L2-mixingales that seems to have gone unnoticed in the econometrics literature, and also a new strong law for Lp-mixingales. These results greatly relax the dependence and heterogeneity conditions relative to the results that are currently cited, at the same time as introducing explicit tradeoffs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.