Wavelets for period analysis of unevenly sampled time series

The wavelet transform shows great promise as a method for period analysis in time series, particularly for detecting the time evolution of the parameters (period, amplitude, phase) describing periodic and pseudo-periodic signals. However, when applied to unevenly sampled time series, the response of the wavelet transform is often more dependent on irregularities in the number and spacing of available data than on actual changes in the parameters of the signal. Yet by casting the wavelet transform as a projection, we can derive its statistical behavior and devise advantageous rescaled transforms. By treating it as a weighted projection to form the weighted wavelet Z-transform (WWZ), we improve its ability to detect, and especially to quantify, periodic and pseudo-periodic signals. The methods are illustrated by analysis of artificial test data, and of the light curves of the variable stars R Aquila and FS Comae.