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This article uses Hong Kong stock market’s four sub-indices to examine the existence and causes of rational expectation bubbles. The unit root test is applied to the rational bubble hypothesis. Various causality test methods are used to examine the causality of bubble among the four sub-indices. The empirical results show that in the sub-periods of 1986 to 2002 and 2000 to 2012, the bubbles of commerce and industry and utilities industries are consistent with rational expectation bubbles, but not so in the finance and properties industries. In general, the rational expectation bubbles in the two sub-periods seemed to have been caused by expectations in other growing foreign economies. [ABSTRACT FROM PUBLISHER]

The stochastic volatility (SV) model can be regarded as a nonlinear state space model. This article proposes the Laplace approximation method to the nonlinear state space representation and applies it for estimating the SV models. We examine how the approximation works by simulations as well as various empirical studies. The Monte Carlo experiments for the standard SV model indicate that our method is comparable to the Monte-Calro Likelihood (MCL; Durbin and Koopman, 1997), Maximum Likelihood (Fridman and Harris, 1998), and Markov chain Monte Carlo (MCMC) methods in the sense of mean square error in finite sample. The empirical studies for stock markets reveal that our method provides very similar estimates of coefficients to those of the MCL. We show a relationship of our Laplace approximation method to importance sampling. [ABSTRACT FROM AUTHOR]