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Mixing properties of harris chains and autoregressive processes

Published online by Cambridge University Press:  24 August 2016

Krishna B. Athreya  and
Sastry G. Pantula
Krishna B. Athreya*
Affiliation:
Iowa State University
Sastry G. Pantula*
Affiliation:
North Carolina State University
*
∗Postal address: Statistical Laboratory, Snedecor Hall, Iowa State University, Ames, IA 50011, USA.
∗∗Postal address: Department of Statistics, North Carolina State University, School of Mathematical Sciences, Box 8203, Raleigh, NC 27695–8203, USA.
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Abstract

Let {Yn: n ≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distribution π (·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

Keywords

STRONG AND UNIFORM MIXINGAUTOREGRESSIVE MOVING-AVERAGE PROCESSESHARRIS-RECURRENT CHAINS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 880 - 892
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported in part by NSF grant DMS-8502311.

References

[1] Andrews, D. W. K. (1984) Non-strong mixing autoregressive processes. J. Appl. Prob. 21, 930–934.Google Scholar
[2] Athreya, K. B. and Ney, P. (1978) A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc. 245, 493–501.CrossRefGoogle Scholar
[3] Athreya, K. B. and Pantula, S. G. (1984) Mixing properties of Harris chains and time series. Institute of Statistics Mimeograph Series No. 1649, North Carolina State University, Raleigh, NC.Google Scholar
[4] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[5] Chanda, K. C. (1974) Strong mixing properties of linear stochastic processes. J. Appl. Prob. 11, 401–408.Google Scholar
[6] Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
[7] Fuller, W. A. (1976) Introduction to Statistical Time Series. Wiley, New York.Google Scholar
[8] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[9] Glynn, P. (1983) . (Some parts available as M. R. C. Technical Reports, Univ. Wisconsin, Madison, WI 53706.) Google Scholar
[10] Ibragimov, I. A. and Linnik, Y. V. (1971) Independent and Stationary Sequences of Random Variables. Walters-Noordhoff, Groningen, The Netherlands.Google Scholar
[11] Lai, T. L. and Wei, C. A. (1982) Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10, 154–166.CrossRefGoogle Scholar
[12] Rosenblatt, M. (1971) Markov Processes, Structure and Asymptotic Behavior. Springer-Verlag, New York.Google Scholar
[13] White, H. and Domowitz, I. (1984) Nonlinear regression with dependent observations. Econometrica 52, 143–161.Google Scholar
[14] Whithers, C. S. (1981) Conditions for linear processes to be strong-mixing. Z. Wahrscheinlichkeitsth. 57, 477–480.CrossRefGoogle Scholar