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Some Properties Of The Maximum Likelihood Estimator In The Simultaneous Switching Autoregressive Model

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  • Seisho Sato
  • Naoto Kunitomo

Abstract

. The simultaneous switching autoregressive (SSAR) model proposed by Kunitomo and Sato (A non‐linearity in economic time series and disequilibrium econometric models. In Theory and Application of Mathematical Statistics (ed. A. Takemura). Tokyo:University of Tokyo Press (in Japanese), 1994; Asymmetry in economic time series and simultaneous switching autoregressive model. Struct. Change Econ. Dyn., forthcoming (1994).) is a Markovian non‐linear time series model. We investigate the finite sample as well as the asymptotic properties of the least squares estimator and the maximum likelihood (ML) estimator. Due to a specific simultaneity involved in the SSAR model, the least squares estimator is badly biased. However, the ML estimator under the assumption of Gaussian disturbances gives reasonable estimates.

Suggested Citation

  • Seisho Sato & Naoto Kunitomo, 1996. "Some Properties Of The Maximum Likelihood Estimator In The Simultaneous Switching Autoregressive Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(3), pages 287-307, May.
    • Handle: RePEc:bla:jtsera:v:17:y:1996:i:3:p:287-307
    DOI: 10.1111/j.1467-9892.1996.tb00277.x
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    Cited by:

    1. Hiroumi Misaki & Naoto Kunitomo, 2013. "On Robust Properties of the SIML Estimation of Volatility under Micro-market noise and Random Sampling," CIRJE F-Series CIRJE-F-892, CIRJE, Faculty of Economics, University of Tokyo.
    2. Naoto Kunitomo & Hiroumi Misaki & Seisho Sato, 2015. "The SIML Estimation of Integrated Covariance and Hedging Coefficient Under Round-off Errors, Micro-market Price Adjustments and Random Sampling," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 333-368, September.
    3. Naoto Kunitomo & Hiroumi Misaki & Seisho Sato, 2015. "The SIML Estimation of Integrated Covariance and Hedging Coefficient under Round-off Errors, Micro-market Price Adjustments and Random Sampling," CIRJE F-Series CIRJE-F-965, CIRJE, Faculty of Economics, University of Tokyo.
    4. Hili, Ouagnina, 2001. "Hellinger distance estimation of SSAR models," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 305-314, June.
    5. Naoto Kunitomo & Seisho Sato, 2001. "A Generalized SSAR Model and Predictive Distribution with an Application to VaR," CIRJE F-Series CIRJE-F-122, CIRJE, Faculty of Economics, University of Tokyo.
    6. Misaki, Hiroumi & Kunitomo, Naoto, 2015. "On robust properties of the SIML estimation of volatility under micro-market noise and random sampling," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 265-281.
    7. Naoto Kunitomo & Hiroumi Misaki, 2013. "The SIML Estimation of Integrated Covariance and Hedging Coefficient under Micro-market noise and Random Sampling," CIRJE F-Series CIRJE-F-893, CIRJE, Faculty of Economics, University of Tokyo.

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