The numerical evaluation of the distribution function of a bilinear from to a quadratic from with econometric examples

This paper considers a general and computationally convenient method of evaluating the distribution function of statistics that are the ratio of a bilinear form to a quadratic form. Numerous Economemc applications of the method are given.     

A NEW FAMILY OF NON-NEGATIVE DISTRIBUTIONS

We introduce a new, flexible family of distributions for non‐negative data, defined by means of a quantile function. We describe some properties of this family, and discuss several methods for estimating the parameters. The distribution is applied to an example from environmental engineering.     

On the connection between orthant probabilities and the first passage time problem

This article describes a new Monte Carlo method for the evaluation of the orthant probabilities by sampling first passage times of a non-singular Gaussian discrete time-series across an absorbing boundary. This procedure makes use of a simulation of several time-series sample paths, aiming to record their first crossing instants. Thus, the computation of the orthant probabilities is traced back to the accurate simulation of a non-singular Gaussian discrete-time series. Moreover, if the simulation is also efficient, this method is shown to be speedier than the others proposed in the literature. As example, we make use of the Davies–Harte algorithm in the evaluation of the orthant probabilities associated to the ARFIMA(0, d, 0) model. Test results are presented that compare this method with currently available software.     

The numerical evaluation of the distribution function of a bilinear from to a quadratic from with econometric examples

This paper considers a general and computationally convenient method of evaluating the distribution function of statistics that are the ratio of a bilinear form to a quadratic form. Numerous Economemc applications of the method are given.     

A test for the presence of conditional heteroskedasticity within arch-m framework

This paper is concerned with testing the presence of ARCH within the ARCH-M model as the alternative hypothesis. Standard testing procedures are inapplicable since a nuisance parameter is unidentified under the null hypothesis. Nonetheless, the diagnostic tests for the presence of the conditional variance is very important since any misspecification in the conditional variance equation leads to inconsistent estimates of the conditional mean parameters. BTo resolve the problem of unidentified nuisance parameter, ‘Ne apply Davies’ approach, and investigate its finite sample performance through a Monte Carlo study.