We give a natural derivation of the inverse Gaussian density and exhibit a specific infinitely divisible distribution obtained by Root's method of stopping Brownian motion with a barrier.

The idea of this paper is to use the multivariate normal inverse Gaussian (MNIG) distribution as the conditional distribution for a multivariate GARCH model. The MNIG distribution belongs to a very ...

Prediction intervals for the inverse Gaussian are obtained from both a frequentist and a Bayesian viewpoint. The frequentist intervals are obtained by constructing pivotals that have the χ 2 and F ...

The usefulness of the MNIG GARCH model is highlighted through a value-at-risk (VAR) application on a portfolio of European, American and Japanese equities. Backtesting shows that for a one-day holding ...