The Lomb-Scargle periodogram (Lomb 1976; Scargle 1982; Press et al. 1988) is perhaps the most frequently applied period search and estimation method in astronomical time series analysis. The application of this method is somewhat restricted, because the underlying model for the data is a single harmonic. Several other methods have been reviewed by Cuypers (1986), while Schwartzenberg-Czerny (1996) and Foster (1996) represent some of the most recent developments. Pelt (1980, 1983, 1992, 1993) developed the general multistage period analysis for irregularly spaced data, where a crude period estimate is first obtained with an approximate pilot-search, and then refined at the subsequent stages. Since the above earlier versions of the multistage method were formulated only for data with equal measurement errors (unity weights), we present here a generalization for the case of unequal measurement errors. The following complementary statistical methods are also presented: the bootstrap for the model parameter error estimates, the evaluation of the modelling statistics with the Kolmogorov-Smirnov test, and the identification of spurious periodicities from real ones with the phase residual regression. Thus the combination of weighted multistage period analysis and complementary statistical tests offers a flexible and powerful tool-set to search for periodicity in a large variety of astronomical time series. A formal presentation of these methods is illustrated on samples of photometric data of two variable stars (V 1794 Cyg and BL Her) and one nonvariable star (SAO50205). The complete data analysis of V 1794 Cyg is presented in Jetsu et al. (1999a, Paper I).
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