Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. These features must be taken into account to produce accurate forecasts of Value-at-Risk (VaR). We provide a comprehensive look at the problem by considering the impact that different distributional assumptions have on the accuracy of both univariate and multivariate GARCH models in out-of-sample VaR prediction. The set of analyzed distributions comprises the normal, Student, Multivariate Exponential Power and their corresponding skewed counterparts. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures used to rank the different specifications. The results show the importance of allowing for heavy-tails and skewness in the distributional assumption with the skew-Student outperforming the others across all tests and confidence levels.
The Multiplicative MIDAS Realized DCC (MMReDCC) model simultaneously accounts for short and long term dynamics in the conditional (co)volatilities of asset returns, in line with the empirical evidence suggesting that their level is changing over time as a function of economic conditions. Herein the applicability of the model is improved along two directions. First, by proposing an algorithm that relies on the maximization of an iteratively re-computed moment-based profile likelihood function and keeps estimation feasible in large dimensions by mitigating the incidental parameter problem. Second, by illustrating a conditional bootstrap procedure to generate multi-step ahead predictions from the model. In an empirical application on a dataset of forty-six equities, the MMReDCC model is found to statistically outperform the selected benchmarks in terms of in-sample fit as well as in terms of out-of-sample covariance predictions. The latter are mostly significant in periods of high market volatility
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