Amplitude and phase changes in the light curves of long-period variables

We describe the derivation of periodicities from visual data for long-period variables, and give expected errors for the derived amplitude, phase and frequency. We extend this analysis by using a moving window to deduce variation in phase and amplitude over time. The method is demonstrated on the Mira-type variable T Cas, and shows evidence that the phase of the first harmonic (period 222.4 d) varies relative to the fundamental (period 444.8 d) with a period of approximately 3000 d. Our analysis parallels, but is completely independent of, the work of Szatmáry, Gál & Kiss and Bedding et al., who both use an approach based on wavelet analysis.