Some weighted mixed portmanteau tests for diagnostic checking in linear time series models

The popular diagnostic checking methods in linear time series models are portmanteau tests based on either residual autocorrelation functions (acf) or partial autocorrelation functions (pacf). In this paper, we device some new weighted mixed portmanteau tests by appropriately combining individual tests based on both acf and pacf. We derive the asymptotic distribution of such weighted mixed portmanteau statistics and study their size and power. It is found that the weighted mixed tests outperform when higher order ARMA models are fitted and diagnostic checks are performed via testing lack of residual autocorrelations. Simulation results suggest to use the proposed tests as complementary to those classical tests found in literature. An illustrative application is given to demonstrate the usefulness of the mixed test.