We develop a factor stochastic volatility model that incorporates leverage effects, return asymmetry, and heavy tails across all systematic and idiosyncratic model components. Our model leads to a flexible high-dimensional dependence structure that allows for time-varying correlations, tail dependence and volatility response to both systematic and idiosyncratic return shocks. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior estimation based on the particle Gibbs, ancestor sampling, particle efficient importance sampling methods and interweaving strategy. To obtain parsimonious specifications in practice, we build computationally efficient model selection directly into our estimation algorithm. We validate the performance of our proposed estimation method via simulation studies with different model specifications. An empirical study for a sample of US stocks shows that return asymmetry is a systematic phenomenon and our model outperforms other factor models for value-at-risk evaluation.

Summary: The unobserved components time series model with stochastic volatility has gained much interest in econometrics, especially for the purpose of modelling and forecasting inflation. We present a feasible simulated maximum likelihood method for parameter estimation from a classical perspective. The method can also be used for evaluating the marginal likelihood function in a Bayesian analysis. We show that our simulation‐based method is computationally feasible, for both univariate and multivariate models. We assess the performance of the method in a Monte Carlo study. In an empirical study, we analyse U.S. headline inflation using different univariate and multivariate model specifications.

We study how the output gap affects potential output over time—i.e., the dynamic hysteresis effect. To do so, we introduce novel unobserved components (UC) models that consider hysteresis as a sequence of lagged effects, thus separating the long-run recession-induced adverse effects from other trend-cycle interactions. The proposed models nest several existing UC models in the literature and accommodate two key characteristics of output dynamics: non-neutrality in the long-run and time-to-build effects. Using Bayesian estimation methods, we find robust evidence supporting the presence of hysteresis effects after the 1970s, with the negative long-run effect of the Global Financial Crisis and the COVID-19 recessions robustly identified. Via Bayesian model averaging, we provide precise and intuitive output gap estimates that highlight the relationship between business cycle fluctuations and the decline in economic growth. Our findings indicate that output trend-cycle decompositions that do not consider hysteresis effects can alter stabilization policy trade-offs.

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.

We propose a structural representation of the correlated unobserved components model, which allows for a structural interpretation of the interactions between trend and cycle shocks. We show that point identification of the full contemporaneous matrix which governs the structural interaction between trends and cycles can be achieved via heteroskedasticity. We develop an efficient Bayesian estimation procedure that breaks the multivariate problem into a recursion of univariate ones. An empirical implementation for the US Phillips curve shows that our model is able to identify the magnitude and direction of spillovers of the trend and cycle components both within-series and between-series.