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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. 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.
    2. 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.
    3. Cizek, P., 2004. "Asymptotics of Least Trimmed Squares Regression," Discussion Paper 2004-72, Tilburg University, Center for Economic Research.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Benedikt M. Pötscher & Ingmar R. Prucha, 1999. "Basic Elements of Asymptotic Theory," Electronic Working Papers 99-001, University of Maryland, Department of Economics.

    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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