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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. Yves F. Atchadé, 2006. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 235-254, June.
    4. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    5. 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.
    6. Benedikt M. Pötscher & Ingmar R. Prucha, 1999. "Basic Elements of Asymptotic Theory," Electronic Working Papers 99-001, University of Maryland, Department of Economics.
    7. 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.
    8. 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;
    All these keywords.

    JEL classification:

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

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