Diagnostic checks in time series models based on a new correlation coefficient of residuals

For checking time series models, the Ljung–Box, Li–Mak and Zhu–Wang statistics play an important role, which use the Pearson's correlation coefficient to implement (squared) residual (partial) autocorrelation tests. In this paper, we replace the Pearson's correlation coefficient with a new rank correlation coefficient and propose a new test statistic to conduct diagnostic checks for residuals in autoregressive moving average models, autoregressive conditional heteroscedasticity models and integer-valued time series models, respectively. We conduct simulations to assess the performance of the new test statistic, and compare it with existing ones, and the results show the superiority of the proposed one. We use three real examples to exhibit its usefulness.