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

Xuexin Wang and Yixiao Sun

Journal of Business & Economic Statistics, 2022, vol. 40, issue 2, 505-521

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.

Date: 2022
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DOI: 10.1080/07350015.2020.1832505

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