Detection of a sinusoidal oscillation of unknownfrequency in a time series – a geodetic approach - Lehmann R. (Journal of Geodetic Science)
Geodetic and geophysical time series may containsinusoidal oscillations of unknown angular frequency.Often it is required to decide if such sinusoidaloscillations are truly present in a given time series. Herewe pose the decision problem as a statistical hypothesistest, an approach very popular in geodesy and other scientificdisciplines. In the case of unknown angular frequenciessuch a test has not yet been proposed.We restrict ourselvesto the detection of a single sinusoidal oscillationin a one-dimensional time series, sampled at non-uniformtime intervals.We compare two solution methods: the likelihoodratio test for parameters in a Gauss-Markov modeland the analysis of the Lomb-Scargle periodogram. Wheneverneeded, critical values of these tests are computedusing the Monte Carlo method. We analyze an exemplarytime series from an absolute gravimetric observation byvarious tests. Finally, we compare their statistical power.It is found that the results for the exemplary time seriesare comparable. The LR test is more flexible, but alwaysrequires the Monte Carlo method for the computation ofcritical values. The periodogram analysis is computationallyfaster, because critical values can be approximatelydeduced from the exponential distribution, at least if thesampling is nearly uniform.