Bayesian modelling of time-varying conditional heteroscedasticity

TL;DR

This paper introduces a Bayesian framework with efficient HMC sampling for estimating time-varying conditional heteroscedastic models, improving analysis of financial data over traditional static models.

Contribution

It develops a Bayesian approach with HMC for time-varying CH models and establishes theoretical posterior contraction rates.

Findings

Better fit for financial data with changing market conditions

Comparable or improved estimation accuracy over frequentist methods

Application to Forex and stock market datasets

Abstract

Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market variability. However we can achieve significantly better insight by considering the time-varying analogues of these models. In this paper, we propose a Bayesian approach to the estimation of such models and develop computationally efficient MCMC algorithm based on Hamiltonian Monte Carlo (HMC) sampling. We also established posterior contraction rates with increasing sample size in terms of the average Hellinger metric. The performance of our method is compared with frequentist estimates and estimates from the time constant analogues. To conclude the paper we obtain time-varying parameter estimates for some popular Forex (currency conversion rate) and stock market datasets.