Testing for spurious and cointegrated regressions: A wavelet approach

This paper proposes a wavelet-based approach to analyze spurious and cointegrated regressions in time series. The approach is based on the properties of the wavelet covariance and correlation in Monte Carlo studies of spurious and cointegrated regression. In the case of the spurious regression, the null hypotheses of zerowavelet covariance and correlation for these series across the scales fail to be rejected. Conversely, these null hypotheses across the scales are rejected for the cointegrated bivariate time series. These nonresidualbased tests are then applied to analyze if any relationship exists between the extraterrestrial phenomenon of sunspots and the earthly economic time series of oil prices. Conventional residual-based tests appear sensitive to the specification in both the cointegrating regression and the lag order in the augmented Dickey– Fuller tests on the residuals. In contrast, the wavelet tests, with their bootstrap t-statistics and confidence intervals, detect the spuriousness of this relationship.