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Strong approximation for cross-covariances of linear variables with long-range dependence

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  • Kouritzin, Michael A.

Abstract

Suppose {[var epsilon]k, -[infinity] = m and otherwise 0), quadratic forms, Whittle's and Hosoya's estimates, adaptive filtering and stochastic approximation.

Suggested Citation

  • Kouritzin, Michael A., 1995. "Strong approximation for cross-covariances of linear variables with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 343-353, December.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:2:p:343-353
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    Cited by:

    1. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2816-2855.
    2. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    3. Kouritzin, Michael A. & Paul, Sounak, 2022. "On almost sure limit theorems for heavy-tailed products of long-range dependent linear processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 208-232.
    4. Ansgar Steland, 2018. "Shrinkage for covariance estimation: asymptotics, confidence intervals, bounds and applications in sensor monitoring and finance," Statistical Papers, Springer, vol. 59(4), pages 1441-1462, December.
    5. Steland, Ansgar & von Sachs, Rainer, 2016. "Asymptotics for High–Dimensional Covariance Matrices and Quadratic Forms with Applications to the Trace Functional and Shrinkage," LIDAM Discussion Papers ISBA 2016038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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