A wavelet approach to multiple cointegration testing

This paper introduces a class of cointegration tests based on estimated low-pass and high-pass regression coefficients from the same wavelet transform of the original time series data.  The procedure can be applied to test the null of cointegration in a n + k multivariate system with n cointegrating relationships without the need of either detrending nor differencing.  The proposed non residual-based wavelet statistics are asymptotically distributed as standard chi-square with nk degrees of freedom regardless of deterministic terms or dynamic regressors, thus offering a simple way of testing for cointegration under the null without the need of special tables.  Small sample quantiles for these wavelet statistics are obtained using Monte Carlo simulation in different situations including I(1) and higher order cointegration cases and it is shown that these wavelet tests exhibit appropriate size and good power when compared to other tests of the null of cointegration.