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On the Ergodicity of First‐Order Threshold Autoregressive Moving‐Average Processes

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  • Kung‐Sik Chan
  • Greta Goracci

Abstract

We introduce a certain Markovian representation for the threshold autoregressive moving‐average (TARMA) process with which we solve the long‐standing problem regarding the irreducibility condition of a first‐order TARMA model. Under some mild regularity conditions, we obtain a complete classification of the parameter space of an invertible first‐order TARMA model into parametric regions over which the model is either transient or recurrent, and the recurrence region is further subdivided into regions of null recurrence or positive recurrence, or even geometric recurrence. We derive a set of necessary and sufficient conditions for the ergodicity of invertible first‐order TARMA processes.

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  • Kung‐Sik Chan & Greta Goracci, 2019. "On the Ergodicity of First‐Order Threshold Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(2), pages 256-264, March.
    • Handle: RePEc:bla:jtsera:v:40:y:2019:i:2:p:256-264
    DOI: 10.1111/jtsa.12440
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    Cited by:

    1. Kung-Sik Chan & Simone Giannerini & Greta Goracci & Howell Tong, 2020. "Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis," Papers 2002.09968, arXiv.org, revised Nov 2021.
    2. Greta Goracci, 2021. "An empirical study on the parsimony and descriptive power of TARMA models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 109-137, March.
    3. Yanglin Li, 2024. "New Unit Root Tests in the Nonlinear ESTAR Framework: The Movement and Volatility Characteristics of Crude oil and Copper Prices," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1757-1776, May.

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