Time Series Analysis in Astronomy: an Application to Quasar Variability Studies

Many astrophysical objects can be associated with continuous non- linear stochastic systems. Up to now, however, the signals coming from these systems have been analyzed mainly through linear approaches, such as the power spectrum (PS) and the structure function (SF) techniques, frequently with controversial results. In this paper we show that in the study of astronomical time series the PS (even in the maximum entropy or CLEAN version) and the SF techniques are often of little use or even misleading, since they do not take into account all the information contained in the data. New techniques, such as the bispectrum and multifractal analyses, are necessary to gain further insight into the dynamics of these systems. The effects of the discrete sampling of the signal are also considered, and the evolution of a single system and that of a multiple subunit system are distinguished. The approach based on phase-space reconstruction algorithms and on dimension and entropy estimators as derived from the theory of nonlinear dynamical systems is discussed as well. In general, the need of developing more and more refined methods of statistical analysis is accompanied by the necessity of possessing an at least approximate a priori knowledge of the dynamics of the system under study.