On weak dependence conditions: The case of discrete valued processes

Paul Doukhan, Konstantinos Fokianos, Xiaoyin Li

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1941-1948
Number of pages8
JournalStatistics and Probability Letters
Issue number11
StatePublished - Nov 1 2012
Externally publishedYes


  • Contraction
  • Dependence
  • Integer autoregressive processes
  • Mixing
  • Thinning operator

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