Kernel-based portmanteau diagnostic test for ARMA time series models

In this paper, the definition of the Toeplitz autocorrelation matrix is used to derive a kernel-based portmanteau test statistic for ARMA models. Under the null hypothesis of no serial correlation, the distribution of the test statistic is approximated by a standard normal using the kernel-based normalized spectral density estimator, without having to specify any alternative model. Unlike most existing portmanteau test statistics, the proposed test is defined for all lags. Simulation studies are conducted to assess the performance of the proposed test. A real application is given to demonstrate the usefulness of this goodness-of-fit test statistic.