Weighted portmanteau statistics for testing for zero autocorrelation in dependent data.

Zero autocorrelation test statistics of the portmanteau type are studied under dependence. The asymptotic distribution of statistics formed with weighted averages of the autocorrelation and partial autocorrelation functions is theoretically obtained and its accuracy is then analyzed via simulation and in an empirical application. In the simulation study, we find that the proposed statistics provide test with sizes quite close to their nominal, intended sizes and with power functions which show high sensitivity to deviations from the null. It also reveals, for all the lags studied, that the tests are increasingly precise as the sample size increases. An application to financial time series modeling is given where the importance of using robust portmanteau statistics is illustrated. Specifically, we show that traditional tests incur in large deviations from their nominal size, whereas robust tests do not.