Tests for Non-Cointegration based on the Frequency Domain

Abstract

This thesis proposes to study the fractional cointegration in the frequency domain. Here is investigated the restrictions that the absence or the presence of cointegration imposes on the determinant of the spectral density matrix of a vector of bivariate series, integrated of order 1, when evaluated at the rst dierence. The errors of the cointegration relationship are allowed to be fractionally integrated. In this study it is shown that the determinant of the spectral density matrix is a power function of the parameter that measures reduction of the order of integration of the error series (denoted here by b) for a set of Fourier frequencies close to the origin. From this, two proposals for the estimation of the cointegrating parameter b are suggested. Tests under the null hypothesis of noncointegration are derived from these estimators and their asymptotic properties are discussed. A nite sample investigation was conducted in order to evaluate the empirical performance of the estimators and tests by calculating the bias, the mean square error, the signicance levels and the power. The results suggest that tests have empirical signicance levels close to nominal levels. Furthermore, the power of the tests shows a similar performance compared with the performance of other classical tests in cointegration literature.