Ricerc@Sapienza

In this paper we investigate different VaR forecasts for daily energy commodities returns using GARCH, EGARCH, GJR-GARCH, Generalized Autoregressive Score (GAS) and the Conditional Autoregressive Value at Risk (CAViaR) models. We further develop a Dynamic Quantile Regression (DQR) one where the parameters evolve over time following a first order stochastic process. The models considered are selected employing the Model Confidence Set procedure of Hansen et al. (2011) which provides a superior set of models by testing the null hypothesis of Equal Predictive Ability.

We consider a dynamical system with small noise for which the drift is parametrized by a finite dimensional parameter. For this model, we consider minimum distance estimation from continuous time observations under lp-penalty imposed on the parameters in the spirit of the Lasso approach, with the aim of simultaneous estimation and model selection. We study the consistency and the asymptotic distribution of these Lasso-type estimators for different values of p. For p = 1, we also consider the adaptive version of the Lasso estimator and establish its oracle properties.