Asymptotic percentage points for Siegel's test statistic for compound periodicities
Andrew T. Walden · Biometrika · 1992
Fisher's test for a periodicity at a single Fourier frequency is often inadequate in practice where it is necessary to test for compound periodicities, i.e. spectral lines at several frequencies. Siegel (1980) derived a test statistic for compound periodicity and provided percentage points for m not exceeding 50, where N = 2m + 1 is the length of the time series. Here the distribution of the test statistic is rewritten to enable computation of exact percentage points for m up to 2000, and accurate empirical interpolation formulae derived. Comparisons are made with two approximating distributions considered by Siegel, namely the noncentral chi-squared distribution with zero degrees of freedom and the Gaussian distribution. It is shown that the Gaussian approximation is very poor, while for m of 50 or more the noncentral chi-squared approximation is excellent.