Estimation of time-varying autoregressive stochastic volatility models with stable innovations

Abstract

A new time-varying autoregressive stochastic volatility model with $$\alpha $$ -stable innovations (TVAR $$\alpha $$ SV) is proposed. This new model for time series data combines a time-varying autoregressive component and a stochastic scaling as known from stochastic volatility models with $$\alpha $$ -stable distributed noise. Hence, the model can cover extreme events better than classical stochastic volatility models. Furthermore, we develop a Gibbs sampling procedure for the estimation of the model parameters. The procedure is based on the estimation strategy by Kim et al. (Rev Econ Stud 65(3): 361–393, 1998) for classical stochastic volatility models, however, the estimation procedure requires a deliberate approximation of $$\alpha $$ -stable distributions by finite mixtures of normal distributions and the application of a simulation smoother for linear Gaussian state space models. A simulation study for the new estimation procedure illustrates the appealing accuracy. Finally, we apply the model to electricity spot price data.