Dynamic mixed models with heterogeneous covariance components using multivariate GARCH innovations and the Dirichlet process mixture

Abstract

This paper presents innovative strategies for correlated data analysis using dynamic mixed effects models to account for the autoregressive conditional-heteroscedasticity of innovations and cross-sectional dependence. In a multivariate setting, the traditional modeling scheme was extended to time-varying components of variances and covariances by initiating the heterogeneous GARCH model. We propose a Bayesian semi-parametric approach by utilizing the centered Dirichlet process as priors for the heterogeneity effects involved in the mean structure. We present a stochastic clustering strategy to distinguish similar patterns of covariates. The Hamiltonian Monte Carlo technique is used to ease the computation of time-series equations for variances and covariances with higher efficiency. We conduct comprehensive simulation studies to examine model features, especially in cluster-wise settings. We adopt the maximal overlap discrete wavelet transforms to isolate short- and long-run sample information for practical applications. The transformation facilitates analyzing the effect of high-frequency or trend variation in macroeconomic factors. We illustrate the advantage of our proposed modeling methodology in the empirical studies by investigating the short-run impacts of macroeconomic events on economic growth and its prediction accounting for the unexpected volatility in the financial market of some selected countries. © 2023 Elsevier B.V.