Optimal Filter Approximations for Latent Long Memory Stochastic Volatility

Abstract

Estimating volatility is a challenging because it is latent, and proxies may not be efficient. Alternative to using the proxies in the conventional time series, there are attempts to filter the latent variable conditional on the realized observations. This paper extends the work of state space method and Markov switching model to approximate long memory stochastic volatility. This encompasses incorporating Whittle approximation to the procedure of conditionally Gaussian observed Markov switching model (CGOMSM) for parameter estimation. Monte Carlo simulations are used to examine the performances of these approaches in terms of their accuracy in parameter estimation as well as the filter estimates. The robustness of these approaches is tested by including some sources of misspecification in the data generating process. It emerges that even in moderately fat-tailed innovations, CGOMSM is efficient as long as the long-range effect is not too large. Due to the consistency in Whittle approximation, the computation time of CGOMSM is significantly shorter, especially when the time series is contaminated with level shifts.