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 analogs of these models. In this paper, we propose a Bayesian approach to the estimation of such models and develop a 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 analogs. To conclude the paper we obtain time-varying parameter estimates for some popular Forex (currency conversion rate) and stock market datasets.
We would like to thank the editor, the associate editor, and two anonymous referees for their constructive suggestions that improved the quality of the manuscript.
"Bayesian Modelling of Time-Varying Conditional Heteroscedasticity." Bayesian Anal. Advance Publication 1 - 29, 2021. https://doi.org/10.1214/21-BA1267