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A central limit theorem for non-instantaneous filters of a stationary Gaussian process

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  • Ho, Hwai-Chung
  • Sun, Tze-Chien

Abstract

A central limit theorem for a class of non-instantaneous filters of a stationary Gaussian process is proved and it is applied to study the limiting distributions of the number of zero-crossings.

Suggested Citation

  • Ho, Hwai-Chung & Sun, Tze-Chien, 1987. "A central limit theorem for non-instantaneous filters of a stationary Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 144-155, June.
    • Handle: RePEc:eee:jmvana:v:22:y:1987:i:1:p:144-155
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    Citations

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    Cited by:

    1. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    2. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.
    3. T. C. Sun, 1997. "Murray Rosenblatt: His Contributions to Probability and Statistics," Journal of Theoretical Probability, Springer, vol. 10(2), pages 279-286, April.
    4. Robinson, P. M., 2001. "The memory of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 101(2), pages 195-218, April.
    5. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, Department of Economics and Business Economics, Aarhus University.
    6. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    7. Sánchez de Naranjo, M. V., 1995. "A central limit theorem for non-linear functionals of stationary Gaussian vector processes," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 223-230, February.
    8. Hidalgo, Javier, 2021. "Bootstrap long memory processes in the frequency domain," LSE Research Online Documents on Economics 106149, London School of Economics and Political Science, LSE Library.
    9. repec:jss:jstsof:05:i07 is not listed on IDEAS

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