THE MARGINAL DENSITY OF BIVARIATE COINTEGRATION ESTIMATORS

Paper number: 94/05

Year: 1994

Paper Category: Discussion Paper

Authors

Karim M.Abadir
University of Exeter

Paolo Paruolo*
University of Bologna

Abstract

The limiting marginal density of efficient estimators of bivariate cointegration vectors is derived in closed form. The formula is exact, and it consists of highly efficient convergent expansion. It is used to plot the density. Furthermore, it is manipulated analytically to reveal features that could not be uncovered by Monte Carlo. For example, it is demonstrated that moments of any integer order exist, and the derived unconditional (marginal) density is compared to the conditional one which is normal.

Keywords: Brownian Motions, Cointegration, Density function, Modified Bessel function, Locally Asymptotically Mixed Normal (LAMN), Monte Carlo (MC).

* This paper was written while the second author was visiting the University of Exeter. We wish to thank Martin Timbrell and Garry Phillips for their help and encouragement.
Correspnding author: Karim Abadir, Department of Economics, Amory Building, Rennes Drive, University of Exeter, Exeter EX4 4RJ. England.
E-Mail:kmabadir@exeter.ac.uk
Phone: England + 392 + 263200
Fax: England + 392 + 263242