Time series models with a common stochastic variance for analysing economic time series

The linear Gaussian state space model for which the common variance is treated as a stochastic time-varying variable is considered for the modelling of economic time series. The focus of this paper is on the simultaneous estimation of parameters related to the stochastic processes of the mean part and the variance part of the model. The estimation method is based on maximum likelihood and it requires the subsequent uses of the Kalman filter to treat the mean part and sampling techniques to treat the variance part. This approach leads to the evaluation of the exact likelihood function of the model subject to simulation error. The standard asymptotic properties of maximum likelihood estimators apply as a result. A Monte Carlo study is carried out to investigate the small-sample properties of the estimation procedure. We present two illustrations which are concerned with the modelling and forecasting of two U.S. macroeconomic time series: inflation and industrial production.