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An asymptotic theory for sample covariances of Bernoulli shifts

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  • Wu, Wei Biao

Abstract

Covariances play a fundamental role in the theory of stationary processes and they can naturally be estimated by sample covariances. There is a well-developed asymptotic theory for sample covariances of linear processes. For nonlinear processes, however, many important problems on their asymptotic behaviors are still unanswered. The paper presents a systematic asymptotic theory for sample covariances of nonlinear time series. Our results are applied to the test of correlations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:453-467
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    References listed on IDEAS

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    1. 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.
    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. Volný, Dalibor, 1993. "Approximating martingales and the central limit theorem for strictly stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 41-74, January.
    4. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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    Cited by:

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    2. 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.
    3. Jirak, Moritz, 2011. "On the maximum of covariance estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1032-1046, July.
    4. Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.
    5. Jirak, Moritz, 2013. "A Darling–Erdös type result for stationary ellipsoids," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1922-1946.
    6. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2022. "Data-driven portmanteau tests for time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 675-698, September.
    7. Zhang, Rongmao & Chan, Ngai Hang, 2018. "Portmanteau-type tests for unit-root and cointegration," Journal of Econometrics, Elsevier, vol. 207(2), pages 307-324.
    8. 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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