A white noise test under weak conditions

Abstract

We consider the well-known white noise test that is available in the literature. Its null distribution is known to be asymptotically normal under different sets of conditions for processes with finite 8th moment. We show that for some specific models, the normality continues to hold under the finiteness of only the 4th moment. This includes various GARCH models, stochastic autoregressive volatility model and autoregressive conditional duration model. Under the alternate hypothesis, for specific models such as infinite order moving average, non-linear moving average and bilinear models with finite 4th moment, we show that with suitable centering and scaling, which is of a different order of magnitude compared to the null case, the test statistic is asymptotically normal.