We introduce a new approximation method for the distribution of functions of random variables that are real-valued. The approximation involves moment matching and exploits properties of the class of normal inverse Gaussian distributions. In the paper we examine the how well the different...

Our objective is volatility forecasting, which is core to many risk management problems. We provide theoretical explanations for (i) the empirical stylized fact recognized at least since Taylor (1986) and Ding, Granger, and Engle (1993) that absolute returns show more persistence than squared...

Here we present a general framework for a GARCH (1,1) type of process with innovations with a probability law of the mean- variance mixing type, therefore we call the process in question the mean variance mixing GARCH \ (1,1) or MVM GARCH\(1,1). One implication is a GARCH\ model with skewed...

In cointegration analysis, when considering a hypothesis of the kind beta =(H_1*phi_1,...,H_n*phi_n) the estimator is a simple switching method that requires starting values. We propose using additional restrictions, then solutions of an eigenvector problem may be used as starting values. Using...

This paper bridges the gap between traditional ARCH modelling and recent advances on realized volatilities. Based on a ten-year sample of five-minute returns for the ECU basket currencies versus the US dollar, we find that the realized volatilities constructed from the summation of the...

In cointegration analysis, when considering a hypothesis of the kind β = (H 1 ϕ 1,..., H n ϕ n) the estimation technique is a simple switching method that requires starting values. Using additional restrictions, the solution of an eigenvector problem may be used as starting values. Using a...

We study regression models that involve data sampled at different frequencies. We derive the asymptotic properties of the NLS estimators of such regression models and compare them with the LS estimators of a traditional model that involves aggregating or equally weighting data to estimate a...