A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation structure between the observation and state innovation vectors and we extend the convolution between the Wishart and the multivariate singular beta distribut...

We propose sparse DCC-GARCH and BEKK-GARCH models based on L 1 ${L}_{1}$ regularization. use the to study daily return volatility correlation spillovers for 24 constituents of Bloomberg commodity index in period 2000–2018. The outperform diagonal out-of-sample terms model fit other criteria. also test whether higher visibility metals energy markets compared with agricultural commodities affects...

This paper introduces the scalar DCC-HEAVY and DECO-HEAVY models for conditional variances correlations of daily returns based on measures realized built from intraday data. Formulas multi-step forecasts are provided. Asymmetric versions developed. An empirical study shows that in terms HEAVY outperform BEKK-HEAVY model covariances BEKK, DCC, DECO multivariate GARCH exclusively

4 GARCH Models 7 4.1 Basic GARCH Specifications . . . . . . . . . . . . . . . . . . . 8 4.2 Diagnostic Checking . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Regressors in the Variance Equation . . . . . . . . . . . . . . . 12 4.4 The GARCH–M Model . . . . . . . . . . . . . . . . . . . . . . 12 4.5 The Threshold GARCH (TARCH) Model . . . . . . . . . . . . 12 4.6 The Exponential GARCH (EG...