|
Abstract:
|
Coherence is traditionally defined with respect to the Fourier spectrum, and relates to the correlation between two processes in the frequency domain. With the advent of increased measurement capability, we are increasingly interested in relaxing the assumption of stationarity and learning how such structures change as a function of time. Unlike the Fourier basis, which cannot adapt to such temporal variation, wavelets provide a powerful tool for representing such processes, and their application to time series is well established. Here, we present coherence for multivariate point-processes under a wavelet framework. We demonstrate that working on continuous data not only reduces information loss due to event aggregation, but by removing the limitations of the Nyquist rate it also enables one to investigate smaller scale variation in the data-streams. In order to estimate the wavelet coherence, temporal smoothing is applied to the individual wavelet spectra. We show this can be equivalently cast into a multi-taper formulation, immediately revealing the wavelet coherence estimator to be asymptotically Goodman distribution with computable degrees of freedom.
|
