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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| Veröffentlicht in: | Journal of business & economic statistics Jg. 40; H. 2; S. 505 - 521 |
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| Sprache: | Englisch |
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Alexandria
Taylor & Francis
03.04.2022
Taylor & Francis Ltd |
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| 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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Xuexin surname: Wang fullname: Wang, Xuexin organization: MOE Key Laboratory of Econometrics, The Wang Yanan Institute for Studies in Economics, Department of Statistics, School of Economics, Fujian Key Lab of Statistics, Xiamen University – sequence: 2 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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