Gregoir, Stéphane and Laroque, Guy (1994) Polynomial cointegration: Estimation and Test. Journal of Econometrics, vol. 63 (n° 1). pp. 183-214.

Abstract

This paper develops statistical tools to analyze the multivariate time series which can be represented with a polynomial error correction model as introduced by Gregoir and Laroque (1993). We propose an identification criterion for the error correction terms, which fits with the estimation procedure. The estimation proceeds in a number of steps, through repeated applications of principal component analysis: test for the overall cointegration dimension and its decomposition into the dimensions of the error correction terms of various degrees, estimation of the error correction terms themselves, and finally estimation of the full model, given the previous results, by ordinary least squares and overall specification test. The asymptotic distribution of the test statistics at each of these various steps is nonstandard, and we provide statistical tables of its main percentiles, for the two cases where there is (or not) a constant term on the right-hand side of the model and the degree of the polynomial error correction terms is at most two