Modelling Volatility Asymmetries: A Bayesian Analysis of a Class of Tree Structured Multivariate Garch Models

Abstract

A new class of multivariate threshold GARCH models is proposed for the analysis and modelling of volatility asymmetries in financial time series. The approach is based on the idea of a binary tree where every terminal node parameterizes a (local) multivariate GARCH model for a specific partition of the data. A Bayesian stochastic method is developed and presented for the analysis of the proposed model consisting of parameter estimation, model selection and volatility prediction. A computationally feasible algorithm that explores the posterior distribution of the tree structure is designed using Markov chain Monte Carlo stochastic search methods. Simulation experiments are conducted to assess the performance of the proposed method, and an empirical application of the proposed model is illustrated using real financial time series.

Keywords: Autoregressive conditional heteroscedasticity, Bayesian inference, Markov chain Monte Carlo, stochastic search, Tree structured models

JEL Classification: C11, C22