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Portmanteau Test and Simultaneous Inference for Serial Covariances

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  • Xiao, Han
  • Wu, Wei Biao

Abstract

The paper presents a systematic theory for asymptotic inferences based on autocovariances of stationary processes. We consider nonparametric tests for se rial correlations using the maximum and the quadratic deviations of sample autocovariances. For these cases, with proper centering and rescaling, the asymptotic distributions of the deviations are Gumbel and Gaussian, respec tively. To establish such an asymptotic theory, as byproducts, we develop a normal comparison principle and propose a sufficient condition for summability of joint cumulants of stationary processes. We adapt a blocks of blocks bootstrapping procedure proposed by Kuensch (1989) and Liu and Singh (1992) to the maximum deviation based tests to improve the finite-sample performance.

Suggested Citation

  • 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".
    • Handle: RePEc:zbw:irtgdp:2019017
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    References listed on IDEAS

    as
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