Time series analysis from a statistical viewpoint

Time series analysis is an enormous field of study in mathematical statistics, econometrics, engineering signal processing, and other fields. This paper gives a brief and incomplete outline of some important themes in this literature that may be helpful in the investigation of variable astronomical phenomena. Autoregressive (ARMA) models can be highly effective for aperiodic but correlated time series as seen in accretion disk systems, active galactic nuclei, and gamma-ray bursts. State space representations, or Kalman filtering, provide a powerful mathematical environment for study of nonstationary, nonlinear, quasi-periodic, unevenly spaced, and Poisson time series in astronomy.