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A New Mixing Condition

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  • Brendan K. Beare

Abstract

In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed ã-mixing. Whereas mixing conditions such as á-mixing are typically defined in terms of entire ó-fields of sets generated by random variables in the distant past and future, ã-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads to a definition of mixing more general than those in current use. A Rosenthal inequality, law of large numbers, and functional central limit theorem are proved for ã-mixing processes.

Suggested Citation

  • Brendan K. Beare, 2007. "A New Mixing Condition," Economics Series Working Papers 348, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:348
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    File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper348.pdf
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    References listed on IDEAS

    as
    1. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    2. Beare, Brendan K., 2009. "A generalization of Hoeffding's lemma, and a new class of covariance inequalities," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 637-642, March.
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    Cited by:

    1. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    2. Beare, Brendan K., 2009. "A generalization of Hoeffding's lemma, and a new class of covariance inequalities," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 637-642, March.

    More about this item

    Keywords

    Mixing; Weak Dependence; Hardy-Krause Variation;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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