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Asymptotic Properties of the Maximum Likelihood Estimator in Regime-Switching Models with Time-Varying Transition Probabilities

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  • Chaojun Li
  • Yan Liu

Abstract

We prove the asymptotic properties of the maximum likelihood estimator (MLE) in time-varying transition probability (TVTP) regime-switching models. This class of models extends the constant regime transition probability in Markov-switching models to a time-varying probability by including information from observations. An important feature in this proof is the mixing rate of the regime process conditional on the observations, which is time varying owing to the time-varying transition probabilities. Consistency and asymptotic normality follow from the almost deterministic geometrically decaying bound of the mixing rate. The assumptions are verified in regime-switching autoregressive models with widely-applied TVTP specifications. A simulation study examines the finite-sample distributions of the MLE and compares the estimates of the asymptotic variance constructed from the Hessian matrix and the outer product of the score. The simulation results favour the latter. As an empirical example, we compare three leading economic indicators in terms of describing U.S. industrial production.

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  • Chaojun Li & Yan Liu, 2020. "Asymptotic Properties of the Maximum Likelihood Estimator in Regime-Switching Models with Time-Varying Transition Probabilities," Papers 2010.04930, arXiv.org, revised Dec 2021.
    • Handle: RePEc:arx:papers:2010.04930
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    References listed on IDEAS

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    1. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    2. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    3. Filardo, Andrew J. & Gordon, Stephen F., 1998. "Business cycle durations," Journal of Econometrics, Elsevier, vol. 85(1), pages 99-123, July.
    4. Siddhartha Chib & Michael J. Dueker, 2004. "Non-Markovian regime switching with endogenous states and time-varying state strengths," Working Papers 2004-030, Federal Reserve Bank of St. Louis.
    5. Demian Pouzo & Zacharias Psaradakis & Martin Sola, 2022. "Maximum Likelihood Estimation in Markov Regime‐Switching Models With Covariate‐Dependent Transition Probabilities," Econometrica, Econometric Society, vol. 90(4), pages 1681-1710, July.
    6. Christian Francq & Michel Roussignol & Jean‐Michel Zakoian, 2001. "Conditional Heteroskedasticity Driven by Hidden Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 197-220, March.
    7. Chang, Yoosoon & Choi, Yongok & Park, Joon Y., 2017. "A new approach to model regime switching," Journal of Econometrics, Elsevier, vol. 196(1), pages 127-143.
    8. Kim, Chang-Jin & Piger, Jeremy & Startz, Richard, 2008. "Estimation of Markov regime-switching regression models with endogenous switching," Journal of Econometrics, Elsevier, vol. 143(2), pages 263-273, April.
    9. Andrew Ang & Geert Bekaert & Min Wei, 2008. "The Term Structure of Real Rates and Expected Inflation," Journal of Finance, American Finance Association, vol. 63(2), pages 797-849, April.
    10. Watson, Mark W, 1994. "Business-Cycle Durations and Postwar Stabilization of the U.S. Economy," American Economic Review, American Economic Association, vol. 84(1), pages 24-46, March.
    11. Bekaert, Geert & Harvey, Campbell R, 1995. "Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
    12. Yao, J., 2001. "On square-integrability of an AR process with Markov switching," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 265-270, April.
    13. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    14. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    15. Kasahara, Hiroyuki & Shimotsu, Katsumi, 2019. "Asymptotic properties of the maximum likelihood estimator in regime switching econometric models," Journal of Econometrics, Elsevier, vol. 208(2), pages 442-467.
    16. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    17. 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.
    18. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
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