An Asymptotic F Test for Uncorrelatedness in the Presence of Time Series Dependence

We propose a simple asymptotic F-distributed Portmanteau test for zero autocorrelations in an otherwise dependent time series. By employing the orthonormal series variance estimator of the variance matrix of sample autocovariances, our test statistic follows an F distribution asymptotically under fixed-smoothing asymptotics. The asymptotic F theory accounts for the estimation error in the underlying variance estimator, which the asymptotic chi-squared theory ignores. Monte Carlo simulations reveal that the F approximation is much more accurate than the corresponding chi-squared approximation in finite samples. Compared with the nonstandard test proposed by Lobato (2001), the asymptotic F test is as easy to use as the chi-squared test: There is no need to obtain critical values by simulations. Further, Monte Carlo simulations indicate that Lobato’s (2001) nonstandard test tends to be heavily undersized under the null and suffers from substantial power loss under the alternatives.