High-Dimensional Sparse Multivariate Stochastic Volatility Models

TL;DR

This paper introduces a fast, penalized OLS-based estimation method for high-dimensional multivariate stochastic volatility models, addressing the curse of dimensionality in Bayesian MCMC approaches.

Contribution

It proposes a novel two-step penalized estimation procedure for MSV models, with proven asymptotic properties and oracle property, improving efficiency in high dimensions.

Findings

Method performs well in simulations

Effective on financial data

Addresses high-dimensional estimation challenges

Abstract

Although multivariate stochastic volatility models usually produce more accurate forecasts compared to the MGARCH models, their estimation techniques such as Bayesian MCMC typically suffer from the curse of dimensionality. We propose a fast and efficient estimation approach for MSV based on a penalized OLS framework. Specifying the MSV model as a multivariate state space model, we carry out a two-step penalized procedure. We provide the asymptotic properties of the two-step estimator and the oracle property of the first-step estimator when the number of parameters diverges. The performances of our method are illustrated through simulations and financial data.