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Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

James Davidson () and Robert de Jong

Econometric Reviews, 1997, vol. 16, issue 3, 251-279

Abstract: This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs 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.

Keywords: Strong law of large numbers; mixing; mixingales; near-epoch dependence; JEL Classification: C19 (search for similar items in EconPapers)
Date: 1997
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