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A proof of consistency of the MLE for nonlinear Markov-switching AR processes

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  • Fermín, Lisandro
  • Marcano, José
  • Rodríguez, Luis-Angel

Abstract

We propose a new approach to demonstrate the consistency of the maximum likelihood estimator for nonlinear Markov-switching AR processes (abbreviated MS-NAR). We obtain a uniform exponential memory loss property for the prediction filter by approximating it by a filter with finite memory. From the α-mixing property for the MS-NAR process we obtain an ergodic theorem. Finally, we show that in the linear and Gaussian case our assumptions are fully satisfied.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:183:y:2022:i:c:s0167715221002911
    DOI: 10.1016/j.spl.2021.109347
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    References listed on IDEAS

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    1. 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.
    2. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    3. 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.
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