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A Simple Asymptotically F-Distributed Portmanteau Test for Time Series Models with Uncorrelated Innovations
Xuexin Wang, Yixiao Sun
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We propose a simple asymptotically F-distributed Portmanteau test for parametric time series models with uncorrelated innovations. Its simplicity comes from an innovative transform of the sample autocovariances of residuals to account for parameters estimation error. Only a consistent estimator is required. Further, 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. A comprehensive Monte Carlo experiment demonstrates that the new Portmanteau test enjoys better size and power balance than other competing tests. An application to the S&P 500 returns illustrates the merits of our testing procedure.
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