Ivan L. Andronov (Department of Astronomy, Odessa State University, Ukraine)
The method of wavelet analysis of irregularly spaced time series
is described based on the least squares fits by using ordinary
and trigonometric polynomials with an additional weight function
making approximation more or less local. Statistical properties
of the test- and smoothing functions and local best fit parameters are
described. It is shown that some local weight functions may give
a compromise between multiple differentiability of the smoothing
parameters (e.g. exp(-c z2),) where z is a dimensionless argument
and c is a coefficient determining the size of the time-frequency
box, and a statistical weight and finite correlation length (for a
rectangular weight function). One among such functions is
w(z)=(1-z2)2 
which is CPU-effective for running parabolae
fits (Andronov I.L., As. Ap. Suppl., 125, 207 (1997)) as well as for
running sine fits. Influence of the shape of w(z) on the
fit parameters is studied. The method is applied to study a- and multi-
periodic variable stars.