A time-varying GARCH mixed-effects model for isolating high- and low- frequency volatility and co-volatility

This article studies long-term, short-term volatility and co-volatility in stock markets by introducing modelling strategies to the multivariate data analysis that deal with serially correlated innovations and cross-section dependence. In particular, it presents an innovative mixed-effects model through a GARCH process, allowing for heterogeneity effects and time-series dynamics. We propose a non-parametric regression model of the penalized low-rank smoothing spline to present time trends into the variance and covariance equations. The strategy provides flexible modelling of the low-frequency volatility and co-volatility in equity markets. The decomposed low-frequency matrix was modelled using the modified Cholesky factorization. The Hamiltonian Monte Carlo technique is implemented as a Bayesian computing process for estimating parameters and latent factors. The advantage of our modelling strategy in empirical studies is highlighted by examining the effect of latent financial factors on a panel across 10 equities over 110 weekly series. The model can differentiate non-parametrically dynamic patterns of high and low frequencies of variance–covariance structural equations and incorporate economic features to predict variabilities in stock markets regarding time-series evidence.