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...

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...

An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable and asymptotically homogeneous functions....

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...