The Cross‐Wavelet Transform and Analysis of Quasi‐periodic Behavior in the Pearson‐Readhead VLBI Survey Sources

Abstract

We introduce an algorithm for applying a cross-wavelet transform to analysis of quasi-periodic variations in a time series and introduce significance tests for the technique. We apply a continuous wavelet transform and the cross-wavelet algorithm to the Pearson-Readhead VLBI survey sources using data obtained from the University of Michigan 26 m paraboloid at observing frequencies of 14.5, 8.0, and 4.8 GHz. Thirty of the 62 sources were chosen to have sufficient data for analysis, having at least 100 data points for a given time series. Of these 30 sources, a little more than half exhibited evidence for quasi-periodic behavior in at least one observing frequency, with a mean characteristic period of 2.4 yr and standard deviation of 1.3 yr. We find that out of the 30 sources, there were about four timescales for every 10 time series, and about half of those sources showing quasi-periodic behavior repeated the behavior in at least one other observing frequency.