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Mixing Conditions, Central Limit Theorems, and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences

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  • Nikolaos Kourogenis
  • Nikitas Pittis

Abstract

This article is a survey of the main results on the central limit theorem (CLT) and its invariance principle (IP) for mixing sequences that have been obtained in the probabilistic literature in the last fifty years or so with a view towards econometric applications. Each of these theorems specifies a set of moment, dependence, and heterogeneity conditions on the underlying sequence that ensures the validity of CLT and IP. Special emphasis is paid to the case in which the underlying sequence has just barely infinite variance, since this case is relevant to econometrics applications that involve high-frequency financial data. Moreover, two new results on IPs that apply to heteroscedastic sequences are obtained. The first IP applies to sequences whose variances evolve over time in a polynomial-like fashion, whereas the second IP concerns sequences that experience a single variance break at some point within the sample.

Suggested Citation

  • Nikolaos Kourogenis & Nikitas Pittis, 2011. "Mixing Conditions, Central Limit Theorems, and Invariance Principles: A Survey of the Literature with Some New Results on Heteroscedastic Sequences," Econometric Reviews, Taylor & Francis Journals, vol. 30(1), pages 88-108.
  • Handle: RePEc:taf:emetrv:v:30:y:2011:i:1:p:88-108
    DOI: 10.1080/07474938.2011.520569
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    Citations

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    Cited by:

    1. Antonios Antypas & Phoebe Koundouri & Nikolaos Kourogenis, 2010. "Aggregational Gaussianity And Barely Infinite Variance In Crop Prices," DEOS Working Papers 1001, Athens University of Economics and Business.
    2. Antypas, Antonios & Koundouri, Phoebe & Kourogenis, Nikolaos, 2013. "Aggregational Gaussianity and barely infinite variance in financial returns," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 102-108.
    3. Lee, Sanghoon & Li, Qiang, 2013. "Uneven landscapes and city size distributions," Journal of Urban Economics, Elsevier, vol. 78(C), pages 19-29.

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