Detecting periodic oscillations in astronomy data: revisiting wavelet analysis with coloured and white noise

The intrinsic random variability of an astronomical source hampers the detection of possible periodicities that we are interested in. We find that a simple first-order autoregressive [AR(1)] process gives a poor fit to the power decay in the observed spectrum for astrophysical sources and geodetic observations. Thus, appropriate background noise models have to be chosen for significance tests to distinguish real features from the intrinsic variability of the source. Here we recall the wavelet analysis with significance and confidence testing but extend it with the generalized Gauss Markov stochastic model as the null hypothesis, which includes AR(1) and a power law as special cases. We exemplify this discussion with real data, such as sunspot number data, geomagnetic indices, X-ray observations, as well as a Global Positioning System (GPS) position time series.