Universal codes as a basis for nonparametric testing of serial independence for time series

Abstract

We address the problem of nonparametric testing of serial independence for time series and its generalization. More precisely, we consider a stationary and ergodic source p , which generates symbols x 1 … x t from some finite set A and a null hypothesis H 0 that p is a Markov source of order at most m , ( m ⩾ 0 ) . The alternative hypothesis H 1 is that the sequence is generated by a stationary and ergodic source, which differs from the source under H 0 . In particular, if m = 0 we have the null hypothesis H 0 that the sequence is generated by a Bernoulli source (i.e. the hypothesis that x 1 … x t are independent). In this paper some new tests that are based on so-called universal codes and universal predictors, are suggested.