On weak dependence conditions: The case of discrete valued processes

Paul Doukhan; Konstantinos Fokianos; Xiaoyin Li

doi:10.1016/j.spl.2012.06.020

On weak dependence conditions: The case of discrete valued processes

Paul Doukhan, Konstantinos Fokianos, Xiaoyin Li

Research output: Contribution to journal › Article › peer-review

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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.

Original language	English (US)
Pages (from-to)	1941-1948
Number of pages	8
Journal	Statistics and Probability Letters
Volume	82
Issue number	11
DOIs	https://doi.org/10.1016/j.spl.2012.06.020
State	Published - Nov 2012
Externally published	Yes

Bibliographical note

Funding Information:
K. Fokianos is partially supported by a Leventis Foundation grant and the paper was completed during a visit at the Department of Mathematics, University Cergy-Pontoise. We also acknowledge the constructive report of the reviewer, as well as O. Wintenberger who helped us improve a previous version and derive Theorem 1 .

Keywords

Contraction
Dependence
Integer autoregressive processes
Mixing
Thinning operator

Publisher link

10.1016/j.spl.2012.06.020

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title = "On weak dependence conditions: The case of discrete valued processes",

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.",

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author = "Paul Doukhan and Konstantinos Fokianos and Xiaoyin Li",

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AU - Fokianos, Konstantinos

AU - Li, Xiaoyin

N1 - Funding Information: K. Fokianos is partially supported by a Leventis Foundation grant and the paper was completed during a visit at the Department of Mathematics, University Cergy-Pontoise. We also acknowledge the constructive report of the reviewer, as well as O. Wintenberger who helped us improve a previous version and derive Theorem 1 .

PY - 2012/11

Y1 - 2012/11

N2 - 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.

AB - 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.

KW - Contraction

KW - Dependence

KW - Integer autoregressive processes

KW - Mixing

KW - Thinning operator

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JO - Statistics and Probability Letters

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On weak dependence conditions: The case of discrete valued processes

Abstract

Bibliographical note

Keywords

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