A Simple Asymptotically F-Distributed Portmanteau Test for Diagnostic Checking of Time Series Models With Uncorrelated Innovations. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Wang, Xuexin; Sun, Yixiao
• Is Part Of: Journal of business & economic statistics. Volume 40:Issue 2(2022)
• Page Start: 505
• Page End: 521
• Publication Date: 2022-04-03
• Subjects: F-distribution -- Fixed-smoothing asymptotics -- Model diagnostics -- Orthonormal series variance estimator -- Parameter estimation uncertainty -- Uncorrelated innovations; Economics -- Statistical methods -- Periodicals; Commercial statistics -- Periodicals; Économie politique -- Méthodes statistiques -- Périodiques; Statistique commerciale -- Périodiques; 330.015195
• DOI: 10.1080/07350015.2020.1832505
• Languages: English
• ISSNs: 0735-0015

Abstract

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.