• Exponential GARCH in mean;
  • Stochastic volatility in mean;
  • Time-varying parameter. JEL C22


This paper introduces and discusses some of the statistical properties of a time-varying parameter stochastic volatility (SV) in mean model. We derive the autocovariance function of an observed series, under the assumption that the conditional variance follows a flexible parameterization, which nests the autoregressive SV and the exponential GARCH specifications. Furthermore, the mean parameter can be time varying. We also present the autocovariance functions of higher orders and discuss identification issues. Our result can be applied so that the properties of the observed data may be compared with the theoretical properties of the models, thus facilitating model identification. Furthermore, they can be employed in the estimation and derivation of misspecification tests.