F-tests for Frequency Modulated Time Series Using Multitaper Methods

Abstract

We propose three new semiparametric multitaper tests for the detection of modulated line components where the modulation is assumed to be created by a polynomial of degree P. The first test, F_4, is a modification of the F-test found in [3] and uses a set of weights to obtain a better in-band concentration for a wider range of tapers. The second test, F_4', builds on the aforementioned test by fixing a problem that arises when choosing to evaluate the F-test with an even number of tapers. We derive the distributions for these two tests along with an examination of the final test based on an aggregation of F_4' tests, where the aggregation is over different multitaper orders. We derive an upper bound for the distribution of the Aggregate F-test statistic, and via simulation, we approximate the F-test's confidence level needed to obtain a pre-specified Type 1 error of the Aggregated test. These new F-tests are compared to the F-test in [3], and [30] via simulation comparing the probability of detecting a frequency-modulated signal in different types of noise and modulation widths. We also examine the functionality of these new test statistics through a study of the SoHO GOLF instrument data.