COVID-19 pandemic is an extreme event that created turmoil in stock markets around the world. This unexpected circumstance poses a critical question of whether the prevailing models can help predict the plummets of indices, hence the returns. In this study, we aim to analyse and forecast the daily stock returns using various generalized autoregressive conditional heteroscedastic (GARCH) models with intertemporal capital asset pricing structure and innovation following (1) a mixture of generalized Pareto and Gaussian distributions and (2) generalized error distribution that can capture extreme events. We also employ the parallel griddy Gibbs (GG) sampling, which is a Markov chain Monte Carlo method, to facilitate parameter estimation. Our simulation study shows that the GG estimation method outperforms the benchmark quasi-maximum likelihood estimation method. We then proceed to the empirical study of seven stock markets where the results from the in-sample period before the COVID-19 pandemic justify the use of the proposed GARCH models. The out-of-sample forecasts during the early COVID-19 period also show satisfactory results.

Electricity price forecasting has been a topic of significant interest since the deregulation of electricity markets worldwide. The New Zealand electricity market is run primarily on renewable fuels, and so weather metrics have a significant impact on electricity price and volatility. In this paper, we employ a mixed-frequency vector autoregression (MF-VAR) framework where we propose a VAR specification to the reverse unrestricted mixed-data sampling (RU-MIDAS) model, called RU-MIDAS-VAR, to provide point forecasts of half-hourly electricity prices using several weather variables and electricity demand. A key focus of this study is the use of variational Bayes as an estimation technique and its comparison with other well-known Bayesian estimation methods. We separate forecasts for peak and off-peak periods in a day since we are primarily concerned with forecasts for peak periods. Our forecasts, which include peak and off-peak data, show that weather variables and demand as regressors can replicate some key characteristics of electricity prices. We also find the MF-VAR and RU-MIDAS-VAR models achieve similar forecast results. Using the LASSO, adaptive LASSO, and random subspace regression as dimension-reduction and variable selection methods helps to improve forecasts where random subspace methods perform well for large parameter sets while the LASSO significantly improves our forecasting results in all scenarios.

This article proposes a new approach to analyze multiple vector autoregressive (VAR) models that render us a newly constructed matrix autoregressive (MtAR) model based on a matrix-variate normal distribution with two covariance matrices. The MtAR is a generalization of VAR models where the two covariance matrices allow the extension of MtAR to a structural MtAR analysis. The proposed MtAR can also incorporate different lag orders across VAR systems that provide more flexibility to the model. The estimation results from a simulation study and an empirical study on macroeconomic application show favorable performance of our proposed models and method.