The analysis of indexed astronomical time series - V. Fitting sinusoids tohigh-speed photometry

The estimation of the frequency, amplitude and phase of a sinusoid from obs ervations contaminated by correlated noise is considered. It is assumed tha t the observations are regularly spaced, but may suffer missing values or l ong time stretches with no data. The typical astronomical source of such da ta is high-speed photoelectric photometry of pulsating stars. The study of the observational noise properties of nearly 200 real data sets is reported : noise can almost always be characterized as a random walk with superposed white noise. A scheme for obtaining weighted non-linear least-squares esti mates of the parameters of interest, as well as standard errors of these es timates, is described. Simulation results are presented for both complete a nd incomplete data. It is shown that, in finite data sets, results are sens itive to the initial phase of the sinusoid.