  The expert system for time series analysis of irregularly spaced signals is
reviewed. It consists of a number of complementary algorithms and programs,
which may be effective for different types of variability. Obviously, for a
pure sine signal, all the methods should produce the same results. However, for
irregularly spaced signals with a complicated structure, e.g. a sum of
different components, different methods may produce significantly different
results.
  The basic approach is based on classical method of the least squares
(1994OAP.....7...49A). However, contrary to common "step-by-step" methods of
removal important components (e.g. mean, trend ("detrending"), sine wave
("prewhitening"), where covariations between different components are ignored,
i.e. erroneously assumed to be zero, we use complete mathematical models.
  Some of the methods are illustrated on the observations of the semi-regular
pulsating variable RY UMa. The star shows a drastic cyclic change of
semi-amplitude of pulsations between 0.01 to 0.37mag, which is interpreted as a
bias between the waves with close periods and a beat period of 4000d (11yr).
The dominating period has changed from 307.35(8)d before 1993 to 285.26(6)d
after 1993. The initial epoch of the maximum brightness for the recent interval
is 2454008.8(5). It is suggested that the apparent period switch is due to
variability of amplitudes of these two waves and an occasional swap of the
dominating wave.
