Application of cubic splines to the spectral analysis of unequally spaced data

Abstract

In the absence of a priori information, nonparametric statistical techniques are often useful in exploring the structure of data. A least-squares fitting program, based on cubic B-splines has been developed to analyze the periodicity of variable star light curves. This technique takes advantage of the limited domain within which a particular B-spline is nonzero to substantially reduce the number of calculations needed to generate the regression matrix. By using simple approximations adapted to modern computer workstations, the computational speed is competitive with most other common methods that have been described in the literature. Since the number of arithmetic operations increases as N<SUP>2</SUP>, where N is the number of data points, this method cannot compete with the fast Fourier transformations (FFT) modification of the Lomb-Scargle algorithm. However, for data sets with N less than 10<SUP>4</SUP>, it should be quite useful. Examples are shown, taken from the Massive Compact Halo Object (MACHO) experiment.