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Paper: Statistically Optimal Approximations of Astronomical Signals: Implications to Classification and Advanced Study of Variable Stars
Volume: 505, Astronomical Surveys and Big Data
Page: 101
Authors: Andronov, I. L.; Chinarova, L. L.; Kudashkina, L. S.; Marsakova, V. I.; Tkachenko, M. G.
Abstract: We have elaborated a set of new algorithms and programs for advanced time series analysis of (generally) multi-component multi-channel observations with irregularly spaced times of observations, which is a common case for large photometric surveys. Previous self-review on these methods for periodogram, scalegram, wavelet, autocorrelation analysis as well as on “running” or “sub-interval” local approximations were self-reviewed in (2003ASPC..292..391A). For an approximation of the phase light curves of nearly-periodic pulsating stars, we use a Trigonometric Polynomial (TP) fit of the statistically optimal degree and initial period improvement using differential corrections (1994OAP.....7...49A). For the determination of parameters of “characteristic points” (minima, maxima, crossings of some constant value etc.) we use a set of methods self-reviewed in 2005ASPC..335...37A, Results of the analysis of the catalogs compiled using these programs are presented in 2014AASP....4....3A. For more complicated signals, we use “phenomenological approximations” with “special shapes” based on functions defined on sub-intervals rather on the complete interval. E. g. for the Algol-type stars we developed the NAV (“New Algol Variable”) algorithm (2012Ap.....55..536A, 2012arXiv1212.6707A, 2015JASS...32..127A), which was compared to common methods of Trigonometric Polynomial Fit (TP) or local Algebraic Polynomial (A) fit of a fixed or (alternately) statistically optimal degree. The method allows determine the minimal set of parameters required for the “General Catalogue of Variable Stars”, as well as an extended set of phenomenological and astrophysical parameters which may be used for the classification. Totally more that 1900 variable stars were studied in our group using these methods in a frame of the “Inter-Longitude Astronomy” campaign (2010OAP....23....8A) and the “Ukrainian Virtual Observatory” project (2012KPCB...28...85V).
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