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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.

Suggested Citation

  • James Davidson & Robert de Jong, 1997. "Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 251-279.
  • Handle: RePEc:taf:emetrv:v:16:y:1997:i:3:p:251-279
    DOI: 10.1080/07474939708800387
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    Citations

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    Cited by:

    1. Yves Atchade, 2005. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," RePAd Working Paper Series LRSP-WP1, Département des sciences administratives, UQO.
    2. 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 1-7.
    3. Shin Kanaya, 2016. "Convergence rates of sums of a-mixing triangular arrays: with an application to non-parametric drift function estimation of continuous-time processes," CREATES Research Papers 2016-24, Department of Economics and Business Economics, Aarhus University.
    4. 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.
    5. Benedikt M. Pötscher & Ingmar R. Prucha, 1999. "Basic Elements of Asymptotic Theory," Electronic Working Papers 99-001, University of Maryland, Department of Economics.
    6. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed-frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    7. Cizek, P., 2004. "Asymptotics of Least Trimmed Squares Regression," Discussion Paper 2004-72, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

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

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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