We show that the full asymptotic distribution for Watson’s statistic, modified for discrete data, can be computed by standard methods. Previous approximate percentiles for the uniform multinomial case are found to be accurate. More extensive percentiles are presented for this distribution, and...

We show that the full asymptotic null distribution for Watson’s 2N U statistic, modified for discrete data, can be computed simply and exactly by standard methods. Previous approximate quantiles for the uniform multinomial case are found to be accurate. More extensive quantiles are presented...

We consider the relative merits of various saddlepoint approximations for the c.d.f. of a statistic with a possibly non-normal limit distribution. In addition to the usual Lugannani-Rice approximation we also consider approximations based on higher-order expansions, including the case where the...

A spurious regression model is one in which the dependent and independent variables are non-stationary, but not cointegrated, and the data are not filtered (e.g., by differencing) before the model is estimated. It is well known that in this case the asymptotic behaviour of the least squares...

A “spurious regression” is one in which the time-series variables are non-stationary and independent. It is well-known that in this context the OLS parameter estimates and the R2 converge to functionals of Brownian motions; the “t-ratios” diverge in distribution; and the Durbin-Watson...

We consider estimating the linear regression model’s coefficients when there is uncertainty about coefficient restrictions. Theorems establish that the mean squared errors of combination estimators, formed as weighted averages of the ordinary least squares and one or more restricted least...

Crude oil markets are highly volatile and risky. Extreme value theory (EVT), an approach to modelling and measuring risks under rare events, has seen a more prominent role in risk management in recent years. This paper presents an application of EVT to the daily returns of crude oil prices in...

We develop a nonlinear mathematical optimization program for investigating the economic and environmental implications of wind penetration in electrical grids and evaluating how hydropower storage could be used to offset wind power intermittence. When wind power is added to an electrical grid...

A load balance model is used to quantify the economic and environmental effects of integrating wind power into three typical generation mixtures. System operating costs over a specified period are minimized by controlling the operating schedule of existing power generating facilities for a range...