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

Xuexin Wang and Yixiao Sun

Journal of Time Series Analysis, 2020, vol. 41, issue 4, 536-550

Abstract: We propose a simple asymptotically 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. The asymptotic F test is as easy to use as the chi‐squared test: there is no need to obtain critical values by simulations. Furthermore, it has more accurate empirical sizes and substantial power advantages, comparing to other competitors.

Date: 2020
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