Maximum Likelihood Estimation of Stochastic Volatility Models
Siem Jan Koopman
This paper presents a Monte Carlo maximum likelihood method of estimating Stochastic Volatility (SV). The basic SV model can be expressed as a linear state space model with log chi-square disturbances. Assuming the Gaussianity of these disturbances, application of the Kalman filter leads to consistent but inefficient Quasi- Maximum Likelihood (QML) estimation. Addressing this problem the present paper shows how arbitrarily close approximations to the exact likelihood function can be constructed by means of importance sampling. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favourably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Markov Chain Monte Carlo (MCMC) method.
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