An F-Test for Polynomial Frequency Modulation

We propose a semi-parametric multitaper F -test for the detection of line components which have been modulated by a polynomial of a given degree. The test is based on one proposed by Thomson in his 2009 paper, "Polymomial Phase Demodulation in Multitaper Analysis." We give the asymptotic null distribution of our test statistic as F with degrees of freedom depending on the modulating polynomial degree, p, and the number of tapers used, K. We demonstrate the performance of our F -test via simulation, and we apply our F -test to optical solar data obtained by the Global Oscillations for Low Frequencies (GOLF) instrument onboard the SOHO solar observatory satellite.