Semiparametric Bayesian Inference of Long‐Memory Stochastic Volatility Models

Abstract

Abstract. In this paper, a semiparametric, Bayesian estimator of the long‐memory stochastic volatility model's fractional order of integration is presented. This new estimator relies on a highly efficient, Markov chain Monte Carlo (MCMC) sampler of the model's posterior distribution. The MCMC algorithm is set forth in the time‐scale domain of the stochastic volatility model's wavelet representation. The key to and centerpiece of this new algorithm is the quick and efficient multi‐state sampler of the latent volatility's wavelet coefficients. A multi‐state sampler of the latent wavelet coefficients is only possible because of the near‐independent multivariate distribution of the long‐memory process's wavelet coefficients. Using simulated and empirical stock return data, we find that our algorithm produces uncorrelated draws of the posterior distribution and point estimates that rival existing long‐memory stochastic volatility estimators.