A Simulation Smoother For Long Memory Time Series With Correlated And Heteroskedastic Additive Noise

The purpose of this paper is to extend the work of So (1999) by accommodating heteroskedasticity in long memory processes and correlation in disturbances. We propose an alternative representation of long memory processes from which we develop filtering equations, prediction densities and a simulation smoother for latent state variables as in the classical Kalman filter. We illustrate the simulation smoother introduced in this paper by estimating a class of long memory models with heteroskedastic correlated additive noises.