SOME PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE SIMULTANEOUS SWITCHING AUTOREGRESSIVE MODEL

Seisho Sato and Naoto Kunitomo

Journal of Time Series Analysis, 1996, vol. 17, issue 3, 287-307

Abstract: 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.

Date: 1996
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