A Simple Hypothesis Test for Heteroscedasticity

Abstract: The scope of this paper is the presentation of a simple hypothesis test that enables to discern heteroscedastic data from homoscedastic i.i.d. gaussian white noise. The main feature will be a test statistic that’s easy applicable and serves well in committing such a test. The power of the statistic will be underlined by examples where it is applied to stock market data and time series from deterministic diffusion a chaotic time series process. It will turn out that in those cases the statistic rejects with a high degree of confidence the random walk hypothesis and is therefore highly reliable. Furthermore it will be discussed, that the test in most cases also may serve as a test for independence and heteroscedasticity in general. This will be exemplified by independent and equally distributed random numbers.