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

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  • James Davidson
  • Robert de Jong

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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 16 (1997)
Issue (Month): 3 ()
Pages: 251-279

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Handle: RePEc:taf:emetrv:v:16:y:1997:i:3:p:251-279

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Related research

Keywords: Strong law of large numbers; mixing; mixingales; near-epoch dependence; JEL Classification: C19;

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Cited by:
  1. Giovanni Cerulli, 2012. "Are R&D Subsidies Provided Optimally? Evidence from a Simulated Agency-Firm Stochastic Dynamic Game," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(1), pages 7.
  2. J. Isaac Miller, 2007. "Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error," Working Papers 0722, Department of Economics, University of Missouri, revised 15 Apr 2009.
  3. Benedikt M. Pötscher & Ingmar R. Prucha, 1999. "Basic Elements of Asymptotic Theory," Electronic Working Papers 99-001, University of Maryland, Department of Economics.
  4. Yves Atchade, 2005. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," RePAd Working Paper Series LRSP-WP1, DĂ©partement des sciences administratives, UQO.

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