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Consistent Estimation of Linear and Non‐linear Autoregressive Models with Markov Regime

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  • Vikram Krishnamurthy
  • Tobias Ryden

Abstract

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time‐point is given by a (non‐observable) Markov chain. We examine maximum likelihood estimation for such models and show consistency of a conditional maximum likelihood estimator. Also identifiability issues are discussed

Suggested Citation

  • Vikram Krishnamurthy & Tobias Ryden, 1998. "Consistent Estimation of Linear and Non‐linear Autoregressive Models with Markov Regime," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 291-307, May.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:3:p:291-307
    DOI: 10.1111/1467-9892.00093
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    Cited by:

    1. 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.
    2. Constantino Hevia & Ivan Petrella & Martin Sola, 2022. "Bond Risk Premia, Priced Regime Shifts, and Macroeconomic Fundamentals," Working Papers 200, Red Nacional de Investigadores en Economía (RedNIE).
    3. David E. Allen & Chialin Chang & Michael McAleer & Abhay K Singh, 2018. "A cointegration analysis of agricultural, energy and bio-fuel spot, and futures prices," Applied Economics, Taylor & Francis Journals, vol. 50(7), pages 804-823, February.
    4. Fermín, Lisandro & Marcano, José & Rodríguez, Luis-Angel, 2022. "A proof of consistency of the MLE for nonlinear Markov-switching AR processes," Statistics & Probability Letters, Elsevier, vol. 183(C).
    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. De Gooijer, Jan G. & Henter, Gustav Eje & Yuan, Ao, 2022. "Kernel-based hidden Markov conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).

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