Accurate prediction of risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) requires precise estimation of the tail of the predictive distribution. Two novel concepts are introduced that offer a specific focus on this part of the predictive density: the censored posterior, a...

We introduce the class of FloGARCH models in this paper. FloGARCH models provide a parsimonious joint model for low frequency returns and realized measures and are sufficiently flexible to capture long memory as well as asymmetries related to leverage effects. We analyze the performances of the...

In this article we derive conditions which ensure the non-negativity of the conditional variance in the Hyperbolic GARCH(p; d; q) (HYGARCH) model of Davidson (2004). The conditions are necessary and sufficient for p < 2 and sufficient for p > 2 and emerge as natural extensions of the inequality constraints derived in...</2>

A sequential Monte Carlo method for estimating GARCH models subject to an unknown number of structural breaks is proposed. Particle filtering techniques allow for fast and efficient updates of posterior quantities and forecasts in real time. The method conveniently deals with the path dependence...

This paper provides empirical evidence that combinations of option implied and time series volatility forecasts that are conditional on current information are statistically superior to individual models, unconditional combinations, and hybrid forecasts. Superior forecasting performance is...

In this article we derive conditions which ensure the non-negativity of the conditional variance in the Hyperbolic GARCH(p,d,q) (HYGARCH) model of Davidson (2004). The conditions are necessary and sufficient for p=1 and sufficient for p=2 and emerge as natural extensions of the inequality...

We propose a flexible GARCH-type model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B-splines of lagged observations and volatilities. Estimation of such a B-spline basis expansion is constructed within the likelihood framework...

A set of multivariate GARCH models is estimated and its empirical validity is compared from the calculation of the Value at Risk. Data used are the daily returns of the nominal exchange rate of the Colombian peso vis-a-vis the American dollar, euro, sterling and Japanese yen for the period...

Forecasting-volatility models typically rely on either daily or high frequency (HF) data and the choice between these two categories is not obvious. In particular, the latter allows to treat volatility as observable but they suffer of many limitations. HF data feature microstructure problem,...

This paper proposes and analyzes tests that can be used to compare the accuracy of alternative conditional density forecasts of a variable. The tests are also valid in the broader context of model selection based on out-of-sample predictive ability. We restrict attention to the case of density...