On weak dependence conditions: The case of discrete valued processes

Paul Doukhan, Konstantinos Fokianos and Xiaoyin Li

Statistics & Probability Letters, 2012, vol. 82, issue 11, 1941-1948

Abstract: 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.

Keywords: Contraction; Dependence; Integer autoregressive processes; Mixing; Thinning operator (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spl.2012.06.020

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