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

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.     

The SIML estimation of realized volatility of the Nikkei-225 Futures and hedging coefficient with micro-market noise

For the estimation problem of the realized volatility and hedging coefficient by using high-frequency data with possibly micro-market noise, we use the Separating Information Maximum Likelihood (SIML) method, which was recently developed by Kunitomo and Sato [11], [12] and [13]. By analyzing the Nikkei-225 Futures data, we found that the estimates of realized volatility and the hedging coefficients have significant bias by using the traditional historical method which should be corrected. The SIML method can handle the bias problem in the estimation by removing the possible micro-market noise in multivariate high-frequency data. We show that the SIML method has the asymptotic robustness under non-Gaussian cases even when the market noises are autocorrelated and endogenous with the efficient market price or the signal term.