Abstract
The classical autocorrelation function might not be very informative when measuring a dependence in binary time series. Recently, alternative tools, namely the autopersistence functions (APF) and their sample counterparts, the autpersistence graphs (APG), have been proposed for the analysis of dependent dichotomous variables.
In this article, we summarize properties of the autopersistence functions for general binary series as well as for some important particular cases. We suggest a normalized version of APF which might be more convenient for a practical use.
The asymptotic properties of autopersistence graphs are investigated. The consistency and asymptotic normality is discussed.
The theoretical results are illustrated by a simulation study.