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Testing For Common Roots

C. Gourieroux
A. Monfort
E. Renault

Abstract

In this paper we propose a procedure for testing commoh roots hypothesis for polynomials in lag operator. Using a generalized Bezout property, we first show that this hypothesis can be written in a "mixed" form, i.e. as a set of equations linking the parameters of interest (the coefficients of the polynomials) and a set of auxiliary parameters. This mixed form is particulary convenient since it is bilinear with respect to these two sets of parameters. This implies, in particular, that for a given null hypothesis a generalized Wald test can be implemented by using O.L.S. and G.L.S. techniques. A sequence of such tests is then proposed and studied.