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

Author

Listed:
  • Ahmed, M. F..
  • Satchell, S

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; these 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 become 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

  • Ahmed, M. F.. & Satchell, S, 2019. "Some Dynamic and Steady-State Properties of Threshold Autoregressions with Applications to Stationarity and Local Explosivity," Cambridge Working Papers in Economics 1923, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1923
    Note: mfa30
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    File URL: http://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe1923.pdf
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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.

    More about this item

    Keywords

    Threshold Auto-regression; Markov process;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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