On a Simple Two-Stage Closed-form Estimator for a Stochastic Volatility in a General Linear Regression

Abstract

In this paper, we consider the estimation of volatility parameters in the context of a linear regression where the disturbances follow a stochastic volatility (SV) model of order one with Gaussian log-volatility. The linear regression represents the conditional mean of the process and may have a fairly general form, including for example finite-order autoregressions. We provide a computationally simple two-step estimator available in closed form. Under general regularity conditions, we show that this two-step estimator is asymptotically normal. We study its statistical properties by simulation, compare it with alternative generalized method-of-moments (GMM) estimators, and present an application to the S&P composite index.

Citation

Dufour, J.-M. and Valéry, P. (2006), "On a Simple Two-Stage Closed-form Estimator for a Stochastic Volatility in a General Linear Regression", Terrell, D. and Fomby, T.B. (Ed.) Econometric Analysis of Financial and Economic Time Series (Advances in Econometrics, Vol. 20 Part 1), Emerald Group Publishing Limited, Leeds, pp. 259-288. https://doi.org/10.1016/S0731-9053(05)20010-5