Bayesian Estimation and Prediction of Stochastic Volatility Models via INLA

Abstract

In this article, we assess Bayesian estimation and prediction using integrated Laplace approximation (INLA) on a stochastic volatility (SV) model. This was performed through a Monte Carlo study with 1,000 simulated time series. To evaluate the estimation method, two criteria were considered: the bias and square root of the mean square error (smse). The criteria used for prediction are the one step ahead forecast of volatility and the one day Value at Risk (VaR). The main findings are that the INLA approximations are fairly accurate and relatively robust to the choice of prior distribution on the persistence parameter. Additionally, VaR estimates are computed and compared for three financial time series returns indexes.

Keywords:

• Bayesian methods
• INLA
• Quasi-maximum likelihood
• Stochastic volatility models

Mathematics Subject Classification:

• 62F15
• 62M10

Additional information

Funding

This research was partially supported by FAPESP and Laboratório EPIFISMA for the first author. The second author received support from FAPESP - Brazil, under grant number 2011/22317-0.