Finite sample properties of a QML estimator of stochastic volatility models with long memory

Abstract

In this paper, we analyse the finite sample properties of a Quasi-Maximum Likelihood (QML) estimator of Long Memory Stochastic Volatility models based on the Whittle approximation of the Gaussian likelihood in the frequency domain. We extend previous studies by including in our Monte Carlo design all the parameters in the model and some more realistic cases. We show that for the parameter values usually encountered in practice, the properties of this estimator are such that inference is not reliable unless the sample size is extremely large. We also discuss a problem of nonidentification in the AutoRegressive Long Memory Stochastic Volatility Model when the volatility has a unit root and we show up its effect on the small sample properties of the QML estimators. The paper finishes with the empirical analysis of daily observations of the IBEX35 index of the Madrid Stock Exchange as an illustration of the problems faced when using this estimator with real time series.