A Simple Asymptotically F-Distributed Portmanteau Test for Diagnostic Checking of Time Series Models With Uncorrelated Innovations

We propose a simple asymptotically F-distributed portmanteau test for diagnostically checking whether the innovations in a parametric time series model are uncorrelated while allowing them to exhibit higher-order dependence of unknown forms. A transform of sample residual autocovariances removing th...

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Published in:Journal of business & economic statistics Vol. 40; no. 2; pp. 505 - 521
Main Authors: Wang, Xuexin, Sun, Yixiao
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.04.2022
Taylor & Francis Ltd
Subjects:
F-distribution
Fixed-smoothing asymptotics
Model diagnostics
Orthonormal series variance estimator
Parameter estimation uncertainty
Uncorrelated innovations
ISSN:0735-0015, 1537-2707
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Abstract We propose a simple asymptotically F-distributed portmanteau test for diagnostically checking whether the innovations in a parametric time series model are uncorrelated while allowing them to exhibit higher-order dependence of unknown forms. A transform of sample residual autocovariances removing the influence of parameter estimation uncertainty makes the test simple. Further, by employing the orthonormal series variance estimator, a special sample autocovariances estimator that is asymptotically invariant to parameter estimation uncertainty, we show that the proposed test statistic is asymptotically F-distributed under fixed-smoothing asymptotics. The asymptotic F-theory accounts for the estimation error of the variance estimator that the asymptotic chi-squared theory ignores. Moreover, an extensive Monte Carlo study demonstrates that the F-test has more accurate finite sample size than existing tests with virtually no power loss. An application to S&P 500 returns illustrates the merits of the proposed methodology.
AbstractList We propose a simple asymptotically F-distributed portmanteau test for diagnostically checking whether the innovations in a parametric time series model are uncorrelated while allowing them to exhibit higher-order dependence of unknown forms. A transform of sample residual autocovariances removing the influence of parameter estimation uncertainty makes the test simple. Further, by employing the orthonormal series variance estimator, a special sample autocovariances estimator that is asymptotically invariant to parameter estimation uncertainty, we show that the proposed test statistic is asymptotically F-distributed under fixed-smoothing asymptotics. The asymptotic F-theory accounts for the estimation error of the variance estimator that the asymptotic chi-squared theory ignores. Moreover, an extensive Monte Carlo study demonstrates that the F-test has more accurate finite sample size than existing tests with virtually no power loss. An application to S&P 500 returns illustrates the merits of the proposed methodology.
Author Wang, Xuexin
Sun, Yixiao
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  givenname: Yixiao
  surname: Sun
  fullname: Sun, Yixiao
  organization: Department of Economics, UC San Diego
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SubjectTerms F-distribution
Fixed-smoothing asymptotics
Model diagnostics
Orthonormal series variance estimator
Parameter estimation uncertainty
Uncorrelated innovations
Title A Simple Asymptotically F-Distributed Portmanteau Test for Diagnostic Checking of Time Series Models With Uncorrelated Innovations
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