Robustness of the Ljung-Box Test and its Rank Equivalent
by Patrick Burns.
Abstract: The Ljung-Box test is known to be robust. This paper reports on simulations that show just how robust it is in finite samples. Even so, we demonstrate some practical applications where the robustness of the test fails dramatically. The Ljung-Box test on the ranks of the data provides a suitably robust alternative when the distribution is extremely long-tailed. In particular, the rank Ljung-Box test is highly recommended over the Ljung-Box test for evaluating the adequacy of GARCH models. Simulations also explore properties of the test when applied to binary data. There is some evidence that the test starts to deteriorate as the number of lags exceeds 5% of the length of the series whether or not the data are long-tailed.