A0231
Title: Residual-based cointegration tests between combinations of I(0) and I(1) processes
Authors: Jose Olmo - Universidad de Zaragoza (Spain) [presenting]
Javier Hualde - Universidad Publica de Navarra (Spain)
Abstract: A novel test of cointegration is presented that is consistent under general forms of serial and mutual dependence in the sequence of innovations. This test is based on the mean square error of a regression between standardized versions of the vector of unit root processes. The test is pivotal under the absence of mutual dependence between the innovations and critical values are provided conditional on the number of unit roots in the system. Under mutual dependence, bootstrap methods are proposed to approximate the critical values of the test. The main contribution of this procedure is the ability to detect and differentiate cointegration (between I(1) processes) from trivial cointegration (between I(1) and I(0) processes). Under cointegration, the test statistic converges to zero in probability whereas under trivial cointegration it converges to one. Under the null hypothesis of no cointegration, the test statistic is a random variable defined in the interval (0,1). This approach does not require of normalization of the cointegration relationship between the variables or suitable choices of the dependent variable in the cointegration regression equation. The finite-sample properties of the test in the bivariate and multivariate cases are studied in a Monte-Carlo simulation exercise for a battery of $ARMA(1,1)$ processes and different covariance matrices.
