A NEW METHOD TO ESTIMATE STOCHASTIC VOLATILITY MODELS: A LOG-GARCH APPROACH

Abstract

Changes in asset return variance or volatility over time may be modeled using the GARCH class models or stochastic volatility (SV) models. The log-GARCH models are the logarithmic extension of the GARCH models. The GARCH models are popular and easily estimated. Compared to the GARCH models, the SV models are more general in several respects, but it is well recognized that they are not easy to estimate. In this paper, we derive a log-GARCH representation of a class of SV models, including the ARMA-SV model, and analyze the finite sample properties of a Quasi-Maximum Likelihood (QML) estimator based on the log-GARCH representation. Our Monte Carlo results indicate that their finite sample properties are superior to those of the Generalized Method of Moments estimator and those of the QML estimator based on the Kalman filter; and close to those of the nonlinear filtering maximum likelihood estimator which is a computationally intensive method. We present an empirical example of daily observations on the yen/dollar exchange rate.