Improvement of Simplified Models of Variability of Stars: A review. (arXiv:1902.00963v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Andronov_I/0/1/0/all/0/1">Ivan L. Andronov</a>
Astronomical data are typically irregular in time, e.g. the space
(HIPPARCOS/TYCHO, KEPLER, GAIA, WISE etc.) and ground-based CCD (NSVS, ASAS,
CRTS, SuperWASP etc.) and photographic (Harvard, Sonneberg, Odessa etc.)
photometrical surveys. This leads to cancellation of the conditions, which lead
to the orthogonality of the basic functions, and thus the simplified methods
give biased parameters of the approximations. We have elaborated a series of
algorithms and programs for statistically correct analysis, and have applied
them to 2000+ variable stars of different types. The data were obtained from an
international collaboration in a frame of the “Inter-Longitude Astronomy” (ILA)
campaign. Some highlights of our studies are presented, with an extended list
of our original publications. The main improvements were done: 1) for the
periodogram analysis – the parameters are determined from a complete set of
equations containing the (algebraic polynomial) trend superimposed on the
(multi-) harmonic wave, so no “detrending”, no “prewhitening” are used; 2) for
the approximations – we use additional (multi-) harmonic waves, and also
“special shapes” (patterns) for parts of the light curve, which correspond to
relatively fast changes (minima of the eclipsing binaries, minima and maxima
for the pulsating variables); 3) “auto correlation analysis” (ACF) – taking
into account the bias due to a trend removal (previously – only a subtraction
of the sample mean was taken into account); ACF for the irregularly spaced
data; 4) for the signals with bad coherence, the “scalegram” analysis is
proposed, which allows to estimate a characteristic cycle length and the
amplitude, as well as to provide a realistic approximation; 5) the extension of
the Morlet-type wavelet for more periodic signals and 6) “running” (parabola,
sine) approximations for aperiodic and “nearly periodic” variations,
respectively.
Astronomical data are typically irregular in time, e.g. the space
(HIPPARCOS/TYCHO, KEPLER, GAIA, WISE etc.) and ground-based CCD (NSVS, ASAS,
CRTS, SuperWASP etc.) and photographic (Harvard, Sonneberg, Odessa etc.)
photometrical surveys. This leads to cancellation of the conditions, which lead
to the orthogonality of the basic functions, and thus the simplified methods
give biased parameters of the approximations. We have elaborated a series of
algorithms and programs for statistically correct analysis, and have applied
them to 2000+ variable stars of different types. The data were obtained from an
international collaboration in a frame of the “Inter-Longitude Astronomy” (ILA)
campaign. Some highlights of our studies are presented, with an extended list
of our original publications. The main improvements were done: 1) for the
periodogram analysis – the parameters are determined from a complete set of
equations containing the (algebraic polynomial) trend superimposed on the
(multi-) harmonic wave, so no “detrending”, no “prewhitening” are used; 2) for
the approximations – we use additional (multi-) harmonic waves, and also
“special shapes” (patterns) for parts of the light curve, which correspond to
relatively fast changes (minima of the eclipsing binaries, minima and maxima
for the pulsating variables); 3) “auto correlation analysis” (ACF) – taking
into account the bias due to a trend removal (previously – only a subtraction
of the sample mean was taken into account); ACF for the irregularly spaced
data; 4) for the signals with bad coherence, the “scalegram” analysis is
proposed, which allows to estimate a characteristic cycle length and the
amplitude, as well as to provide a realistic approximation; 5) the extension of
the Morlet-type wavelet for more periodic signals and 6) “running” (parabola,
sine) approximations for aperiodic and “nearly periodic” variations,
respectively.
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