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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Bibliographic Details
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
Online Access:Get full text
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Summary: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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ISSN:0735-0015
1537-2707
DOI:10.1080/07350015.2020.1832505