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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

SummaryTime-varying transition probability (TVTP) regime-switching models extend the constant regime transition probability in Markov-switching models to include information from observations. We show consistency and asymptotic normality of the maximum likelihood estimator (MLE) in general TVTP regime-switching models where the conditional distribution ofdepends on lagged regimes. Consistency of the MLE is also shown under misspecification. 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 asymptotic variance estimates 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.

Suggested Citation

  • Chaojun Li & Yan Liu, 2023. "Asymptotic properties of the maximum likelihood estimator in regime-switching models with time-varying transition probabilities," The Econometrics Journal, Royal Economic Society, vol. 26(1), pages 67-87.
    • Handle: RePEc:oup:emjrnl:v:26:y:2023:i:1:p:67-87.
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    File URL: http://hdl.handle.net/10.1093/ectj/utac022
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