Bayesian Inference of Long-Memory Stochastic Volatility via Wavelets

Abstract

In this paper we are concerned with estimating the fractional order of integration associated with a long-memory stochastic volatility model. We develop a new Bayesian estimator based on the Markov chain Monte Carlo sampler and the wavelet representation of the log-squared returns to draw values of the fractional order of integration and latent volatilities from their joint posterior distribution. Unlike short-memory stochastic volatility models, long-memory stochastic volatility models do not have a state-space representation, and thus their sampler cannot employ the Kalman filters simulation smoother to update the chain of latent volatilities. Instead, we design a simulator where the latent long-memory volatilities are drawn quickly and efficiently from the near independent multivariate distribution of the long-memory volatility's wavelet coefficients. We find that sampling volatility in the wavelet domain, rather than in the time domain, leads to a fast and simulation-efficient sampler of the posterior distribution for the volatility's long-memory parameter and serves as a promising alternative estimator to the existing frequentist based estimators of long-memory volatility.