The concept of a near-integrated vector random process is introduced. Such processes help us to work towards a general asymptotic theory of regression for multiple time series in which some series may be integrated processes of the ARIMA type, others may be stable ARMA processes with near unit...

It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds.

Slowly varying regressors are asymptotically collinear in linear regression. Usual regression formulae for asymptotic standard errors remain valid but rates of convergence are affected and the limit distribution of the regression coefficients is shown to be one dimensional. Some asymptotic...

This paper derives the exact finite sample distribution of the two-stage GLS (generalized least squares) estimator in a multivariate linear model with general linear parameter restrictions. This includes the seemingly unrelated regression (SUR) model as a special case and generalizes presently...

This paper continues the theoretical investigation of Park and Phillips [7]. We develop an asymptotic theory of regression for multivariate linear models that accommodates integrated processes of different orders, nonzero means, drifts, time trends and cointegrated regressors. The framework of...

Recent developments in nonstationary time series and cointegration are discussed and three new books in the area are reviewed. Some perspectives concerning the scope of current interest in the field are provided, and some novel themes for future research are outlined.

A new family of kernels is suggested for use in heteroskedasticity and autocorrelation consistent (HAC) and long run variance (LRV) estimation and robust regression testing. The kernels are constructed by taking powers of the Bartlett kernel and are intended to be used with no truncation (or...

We offer a new and straightforward proof of F.B. Knight's [3] theorem that the Cauchy type is characterized by the fact that it has no atom and is invariant under the involution i : x - -1/x. Our approach uses the representation X = tan theta where theta is uniform on (-pi/2,pi/2) when X is...

The paper considers approximate distribution theory as a way to deliver practical improvements over asymptotic methods. Trials of the adequacy of asymptotic series based approximations are conducted and the results exhibit the need for further improvements. An alternative approach is suggested...

Cramer's inversion formula for the distribution of a quotient is generalized to matrix variates and applied to give an alternative derivation of the matrix t-distribution.