Generalised Wald type tests of nonlinear restrictions

Author:	Zaka Ratsimalahelo, University of Franche-Comté, France
Topic:	9.1 Economic & Business Systems
Session:	Economic and Business Systems
Keywords:	Wald type tests; Matrix perturbation theory; Nonlinear restrictions; Spectral decomposition; Covariance matrix degenerate; Granger causality.

Abstract

This paper proposes a generalised Wald type tests to test the hypothesis of the nonlinear restrictions. We circumvent the problem of singularity of the covariance matrix associated with the usual Wald test by proposing a generalised inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. New threshold values are derived to estimate the rank of the covariance matrix. We also propose an operational procedure to test the hypothesis of the Granger non-causality in cointegrated systems.