A Frequency-domain Based Test for Non-correlation between Stationary Time Series

A one-sided asymptotically normal test for non-correlation between two stationary time series is proposed based on the spectral coherence function. The test statistic is a properly standardized version of the integrated spectral coherency and has similar asymptotic properties as a previously introduced time domain based test for non-correlation. Unlike its time domain counterpart, the proposed test does not require prewhitening of the time series and, thus, is a truly nonparametric test for non-correlation. In a simulation study, we evaluate the small sample performance of the proposed test in comparison with the time domain test and address the problem of bandwidth selection. Furthermore, we present a modification of the test statistic that allows to test for non-correlation over frequency bands. This version shows higher power of detecting interrelationships restricted to the frequency band of interest. This work has been carried out at the Institute of Applied Mathematics at the University of Heidelberg and partly while the author was visiting the Department of Statistics at the University of Chicago.