This paper utilizes asymptotic expansions of the Edgeworth type to investigate alternative forms of the Wald test of nonlinear restricti ons. Some formulae for the asymptotic expansion of the distribution of the Wald statistic are provided for a general case that should include most econometric...

A new procedure for statistical inference in cointegrating regressions is developed. The author introduces canonical cointegrating regressions (regressions formulated with the transformed data). The required transformations involve simple adjustments of the integrated processes using stationary...

The author derives some exact finite sample disbibutions and characterizes the tail behavior of maximum likelihood estimators of the cointegrating coefficients in error correction models. The reduced rank regression estimator has a distribution with Cauchy-like tails and no finite moments of...

This paper is concerned with model determination methods and their use in the prediction of economic time series. The methods are Bayesian but they can be justified by classical arguments as well. The paper continues some recent work on Bayesian asymptotic, develops embedding techniques for...

A limit theory for Wald tests of Granger causality in levels vector autoregressions (VAR's) and error correction models (ECM's) is developed, which allows for stochastic trends and cointegration. Earlier work is extended to the general case, thereby characterizing when these Wald tests are...

A limiting representation of the Bayesian data density is obtained and shown to be the same general exponential form for a wide class of likelihoods and prior distributions. An embedding theorem is given which shows how to embed the exponential density in a continuous time process. From the...

The concept of a near-integrated vector random process is introduce d, helping the author work towards a general asymptotic theory of regression fo r multiple time series in which some series may be integrated processe s of the ARIMA type, others may be stable ARMA processes with near unit...