Local Fits of Signals with Asymptotic Branches

The method of "asymptotic parabola" fit is described, its analytical properties are discussed in comparison with other types of fits. The method is effective for the (possibly highly asymmetric) signals with practically linear ascending and descending branches connected by relatively short transitions at maximum or minimum, e.g. for the brightness variations of pulsating or eclipsing variables or for the phase variations in stars with abrupt period changes. The method is illustrated by an application to the Mira-type star U Her.