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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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    1. Aleem, Abdul & Lahiani, Amine, 2014. "A threshold vector autoregression model of exchange rate pass-through in Mexico," Research in International Business and Finance, Elsevier, vol. 30(C), pages 24-33.
    2. Goodwin, Barry K. & Harper, Daniel C., 2000. "Price Transmission, Threshold Behavior, And Asymmetric Adjustment In The U.S. Pork Sector," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 32(3), pages 1-11, December.
    3. Zha, Tao & Rubio-Ramírez, Juan Francisco & , & Foerster, Andrew, 2013. "Perturbation Methods for Markov-Switching DSGE Models," CEPR Discussion Papers 9464, C.E.P.R. Discussion Papers.
    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    6. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    7. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    8. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    9. Engel, Charles, 1994. "Can the Markov switching model forecast exchange rates?," Journal of International Economics, Elsevier, vol. 36(1-2), pages 151-165, February.
    10. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    11. Andrew Foerster & Juan F. Rubio‐Ramírez & Daniel F. Waggoner & Tao Zha, 2016. "Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 7(2), pages 637-669, July.
    12. Timmermann, Allan, 2000. "Moments of Markov switching models," Journal of Econometrics, Elsevier, vol. 96(1), pages 75-111, May.
    13. González, M., 1997. "Threshold unit root models," DES - Working Papers. Statistics and Econometrics. WS 6214, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    15. Ahmed Muhammad Farid & Satchell Stephen, 2018. "What Proportion of Time is a Particular Market Inefficient? … A Method for Analysing the Frequency of Market Efficiency when Equity Prices Follow Threshold Autoregressions," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-22, July.
    16. Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.
    17. Galyna Grynkiv & Lars Stentoft, 2018. "Stationary Threshold Vector Autoregressive Models," JRFM, MDPI, vol. 11(3), pages 1-23, August.
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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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