Simulated maximum likelihood in autoregressive models with stochastic volatility errors

Abstract

Autoregressive conditional heteroscedastic type and stochastic volatility (SV) models are designed to analyze and model the conditional variance (volatility), but in some contexts the specification of the conditional mean is also important. In this paper we consider a combination model in which the conditional mean is modeled by an autoregressive (AR) model and conditional variance is modeled by an SV model. We call this model an AR(p)-SV model, consider some of its properties, discuss its likelihood, and estimate its parameters using simulated maximum likelihood. We also estimate the volatilities by a particle filter. Then these methods are applied to four financial time series.