Title: Variational approximation for stochastic volatility via continuous random walk processes
Authors: Nicolas Bianco - University of Padova (Italy) [presenting]
Mauro Bernardi - University of Padova (Italy)
Abstract: Discrete-time stochastic volatility (SV) represent a valid alternative to GARCH models, that are easy to estimate, but have relevant drawbacks. However, the formulation of the volatility as a latent process makes parameters estimation more complicated for the SV models. The estimation has been previously tackled within an approximate Bayesian framework by leveraging the variational Bayes approach. One approach locally approximates the underlying stochastic process, while another suggests using a multivariate Gaussian as an approximation of the joint distribution of the latent volatilities with a fixed structure of the variance-covariance matrix. We propose variational methods for parameters estimation and signal extraction in a Bayesian context that relies on a flexible approximation of the volatility through a continuous random walk (CRW) process. The latter is a semi-parametric process that is consistent with respect to the choice of the locations and it has a sparse precision matrix that enables efficient computations. Although the point estimates of the posterior volatility are precise, the CRW process is homoscedastic which is in contrast with the true behaviour of the volatility a posteriori. Therefore, to get accurate HPD intervals, we extend the CRW process to account for the heteroscedastic behaviour by allowing its scale to follow a process leading to a hierarchical random field approximation.