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In spite of enormous amounts of existing software and literature on time series analysis (TSA), only comparatively little work has been done concerning those time series which are most often encountered in astronomy, namely unevenly sampled series. Hence, our first reason for yet another TSA package is to provide tools to handle such series. The second reason is to supply astronomers with modern tools enabling a more complete statistical evaluation of the results than practicized so far.
The interests of galactic and extragalactic astronomers in time series analysis differ markedly. The former are particularly interested in the analysis of genuinely periodic variations, while the latter are more often concerned with stochastic phenomena. We have implemented tools to satisfy the basic needs of both types of users, with emphasis on periodic variations. This chapter provides general guidelines for the user of the MIDAS TSA package. Detailed technical information is provided separately for each command of the package in both Volume A of the MIDAS User Guide and the interactive MIDAS HELP utility.
The present chapter is not meant to be a substitute for a textbook on time series analysis. We recommend the publications by Deeming (1976) and Bloomfield (1976) for a general introduction to TSA and works by Brandt (1970) and Eadie et al. (1971) for the statistical background. Relevant statistical tables are listed in Brandt (1970) and Abramovitz & Stegun (1972), and a code for the computation of the probability functions is provided by Press et al. (1986). However, we do explain the concepts used in the description of our software and point out their statistical context (Sect. 2). We will discuss Fourier analysis as the crucial example of TSA (Sect3). Sect. 4 contains the general description of the MIDAS TSA package and its commands. A summary of the commands and their syntaxes is listed in Sect. 5. Examples of some typical problems and their treatment within MIDAS are given in Sect. 6.
Note that the present TSA package is not in any way related to the former TSA package first implemented in the January 88 release of MIDAS. The ancestor of this new package originally was a stand-alone package developed at Warsaw Observatory and called ULA. It was expanded and converted to MIDAS at the European Southern Observatory in Garching.