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On the maximum of covariance estimators

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  • Jirak, Moritz

Abstract

Let be a stationary process with mean 0 and finite variances, let [phi]h=E(XkXk+h) be the covariance function and its usual estimator. Under mild weak dependence conditions, the distribution of the vector is known to be asymptotically Gaussian for any , a result having important statistical consequences. Statistical inference requires also determining the asymptotic distribution of the vector for suitable d=dn-->[infinity], but very few results exist in this case. Recently, Wu (2009) [19] obtained tail estimates for the vector for some sequences dn-->[infinity] and used these to construct simultaneous confidence bands for , 1

Suggested Citation

  • Jirak, Moritz, 2011. "On the maximum of covariance estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1032-1046, July.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:6:p:1032-1046
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    References listed on IDEAS

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    1. Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.
    2. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2003. "Some Limit Theory For Autocovariances Whose Order Depends On Sample Size," Econometric Theory, Cambridge University Press, vol. 19(5), pages 829-864, October.
    3. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
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    1. Lei Jin & Suojin Wang, 2016. "A New Test for Checking the Equality of the Correlation Structures of two time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 355-368, May.
    2. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    3. Alexander Braumann & Jens‐Peter Kreiss & Marco Meyer, 2021. "Simultaneous inference for autocovariances based on autoregressive sieve bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 534-553, September.
    4. Mayer, Alexander, 2020. "(Consistently) testing strict exogeneity against the alternative of predeterminedness in linear time-series models," Economics Letters, Elsevier, vol. 193(C).
    5. Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.
    6. Jirak, Moritz, 2013. "A Darling–Erdös type result for stationary ellipsoids," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1922-1946.
    7. Xiao, Han & Wu, Wei Biao, 2019. "Portmanteau Test and Simultaneous Inference for Serial Covariances," IRTG 1792 Discussion Papers 2019-017, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

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