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Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity

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  • Muhammad Farid Ahmed

    (Cambridge INET, Faculty of Economics, University of Cambridge, Cambridge CB3 9DD, UK
    Magdalene College, University of Cambridge, Cambridge CB3 0AG, UK
    Department of Economics, Lahore University of Management Sciences, Lahore 54000, Pakistan)

  • Stephen Satchell

    (The University of Sydney Business School, The University of Sydney, Sydney, NSW 2006, Australia
    Trinity College, University of Cambridge, Cambridge CB2 1TQ, UK)

Abstract

The purpose of this paper is to investigate the dynamics and steady-state properties of threshold autoregressive models with exogenous states that follow Markovian processes. Markovian processes are widely used in applied economics although their statistical properties have not been explored in detail. We use characteristic functions to carry out the analysis, and this allows us to describe limiting distributions for processes not considered in the literature previously. We also calculate analytical expressions for some moments. Furthermore, we see that we can have locally explosive processes that are explosive in one regime whilst being strongly stationary overall. This is explored through simulation analysis, where we also show how the distribution changes when the explosive state becomes more frequent although the overall process remains stationary. In doing so, we are able to relate our analysis to asset prices which exhibit similar distributional properties.

Suggested Citation

  • Muhammad Farid Ahmed & Stephen Satchell, 2019. "Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity," JRFM, MDPI, vol. 12(3), pages 1-18, July.
    • Handle: RePEc:gam:jjrfmx:v:12:y:2019:i:3:p:123-:d:250648
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    References listed on IDEAS

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    Cited by:

    1. Yiu-Kuen Tse, 2019. "Editorial for the Special Issue on Financial Econometrics," JRFM, MDPI, vol. 12(3), pages 1-2, September.

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