The Effect of Dependence on Chi Squared Tests of Fit

Abstract

Tests of fit that assume i.i.d. observations may be affected by dependence among the observations. This effect is studied for the Pearson chi squared test when the data form a stationary stochastic process. The general form of asymptotic distribution theory under the null hypothesis is outlined and examples are given. For testing fit to a specified normal law, it is shown that when observations come from a quite general class of Gaussian stationary processes, positive correlation among the observations is confounded with lack of normality.