The Cross-Wavelet Transform and Analysis of Quasiperiodic Behavior in the Pearson-Readhead VLBI Survey Sources

Abstract

We introduce an algorithm for applying a cross-wavelet transform to analysis of quasiperiodic 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 parabloid at observing frequencies of 14.5, 8.0, and 4.8 GHz. Thirty of the sixty-two sources were chosen to have sufficient data for analysis, having at least 100 data points for a given time-series. Of these thirty sources, a little more than half exhibited evidence for quasiperiodic 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 thirty sources, there were about four time scales for every ten time series, and about half of those sources showing quasiperiodic behavior repeated the behavior in at least one other observing frequency.