In this paper, we consider a specification testing problem in nonlinear time series models with nonstationary regressors and propose using a nonparametric kernel-based test statistic. The nullasymptotics for the proposed nonparametric test statistic have been well developed in the existing...

The article treats the reduction of quadratic forms to the normal form by Gauss's method taking in discussing various determinants whose behavior will determine its nature. Applications of this method are illustrated for the most common production functions: Cobb-Douglas and CES.

We derive some new results on the expectation of quadratic forms in normal and nonnormal variables. Using a nonstochastic operator, we show that the expectation of the product of an arbitrary number of quadratic forms in noncentral normal variables follows a recurrence formula. This formula...

We investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate densities, including densities without compact support and...

In this paper, we establish some new central limit theorems for generalized U-statistics of dependent processes under some mild conditions. Such central limit theorems complement existing existing results available from both the econometrics literature and statistics literature. We then look at...

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling...

If permanent output is uncertain, tax smoothing can be perilous: both debt levels and tax rates are difficult to stabilize and may drift upwards. One practical remedy would be to target the debt. However, our simulations confirm that such a policy would require undesirably volatile fiscal...

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling...