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First Order Autoregressive Processes and Strong Mixing

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Abstract

A sufficient condition is given such that first-order autoregressive processes are strong mixing. The condition is specified in terms of the univariate distribution of the independent identically distributed innovation random variables. Normal, exponential, uniform, Cauchy, and many other continuous innovation random variables are shown to satisfy the condition. In addition, an example of a first-order autoregressive process which is not strong mixing is given. This process has Bernoulli (p) innovation random variables and any autoregressive parameter in (0,1/2).

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  • Donald W.K. Andrews, 1983. "First Order Autoregressive Processes and Strong Mixing," Cowles Foundation Discussion Papers 664, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:664
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d06/d0664.pdf
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    Cited by:

    1. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2019. "A General Framework for Prediction in Time Series Models," Papers 1902.01622, arXiv.org.
    2. Tae-Hwan Kim & Dong Jin Lee & Paul Mizen, 2020. "Impulse Response Analysis in Conditional Quantile Models and an Application to Monetary Policy," Working papers 2020rwp-164, Yonsei University, Yonsei Economics Research Institute.
    3. ŁUkasz Lenart & Jacek Leśkow & Rafał Synowiecki, 2008. "Subsampling in testing autocovariance for periodically correlated time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 995-1018, November.
    4. Schumann, Martin & Severini, Thomas A. & Tripathi, Gautam, 2023. "The role of score and information bias in panel data likelihoods," Journal of Econometrics, Elsevier, vol. 235(2), pages 1215-1238.
    5. Luz M. Gómez & Rogério F. Porto & Pedro A. Morettin, 2021. "Nonparametric regression with warped wavelets and strong mixing processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1203-1228, December.
    6. Lee, Dong Jin & Kim, Tae-Hwan & Mizen, Paul, 2021. "Impulse response analysis in conditional quantile models with an application to monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).

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