Universal Codes as a Basis for Nonparametric Testing of Serial Independence for Time Series

Abstract

We consider a stationary and ergodic source $p$ generated symbols $x_1...x_t$ from some finite set $A$ and a null hypothesis $H_0$ that $p$ is Markovian source with memory (or connectivity) not larger than $m,(m>=0).$ 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 Bernoully source (or the hypothesis that $x_1...x_t$ are independent.) Some new tests which are based on universal codes and universal predictors, are suggested.

accepted for ISIT'05

References in corpus (1)

• Weakly Convergent Nonparametric Forecasting of Stationary Time Series