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 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.