Indirect Inference for Stochastic Volatility Models via the Log-Squared Observations

Abstract

An indirect estimator of the stochastic volatility (SV) model with AR(1) logvolatility is proposed. The estimator is derived as an application of the method of indirect inference (Gouriéroux, Monfort and Renault (1993)), using an auxiliary SV model that mimics the SV model of interest (which has latent volatility) but is constructed so as to make volatility observable. The resulting estimator works by fitting an AR(1) to the log-squared observations and then applying a simple transformation to the parameter estimates. A closed-form expression for the asymptotic covariance matrix of the estimator is also derived. The estimator is applied to the Brussels All Shares Price Index from January 1, 1980, to January 16, 2003.