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On weak dependence conditions: the case of discrete valued processes. (English) Zbl 1254.60036

Stat. Probab. Lett. 82, No. 11, 1941-1948 (2012); corrigendum ibid. 83, No. 2, 674-675 (2013).
Summary: We investigate the relationship between weak dependence and mixing for discrete valued processes. We show that weak dependence implies mixing conditions under natural assumptions. The results specialize to the case of Markov processes. Several examples of integer valued processes are discussed and their weak dependence properties are investigated by means of a contraction principle. In fact, we show the stronger result that the mixing coefficients for infinite memory weakly dependent models decay geometrically fast. Hence, all integer values models that we consider have weak dependence coefficients which decay geometrically fast.

MSC:

60G09 Exchangeability for stochastic processes
60F17 Functional limit theorems; invariance principles
62G05 Nonparametric estimation
62G09 Nonparametric statistical resampling methods
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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