Score based goodness-of-fit tests for time series

This paper studies a class of tests useful for testing goodness of fit of a wide variety of time series models. These tests are based on a class of empirical processes marked by certain scores. Major advantages of these tests are that they are easy to implement, require only weak conditions that are usually satisfied in practical applications, the relevant critical values are readily available without bootstrap, and are more powerful than the Ljung-Box test, the Li-Mak test and the Koul-Stute test in all the cases we have tried. A comparison with the Fan-Zhang test is included. We also extend the class of tests to include score-like statistics.