Hidden frequency estimation with data tapers

The detection and estimation of hidden frequencies has long been recognized as an important problem in time series. In this paper we study the asymptotic theory for two methods of high-precision estimation of hidden frequencies (the secondary analysis method and the maximum periodogram method) using a data taper. In ordinary situations, a data taper may reduce the estimation precision slightly. However, when there are high peaks in the spectral density of the noise or other strong hidden periodicities with frequencies close to the hidden frequency of interest, the procedures for detection of the existence of and estimation of the hidden frequency of interest fail if data are nontapered whereas they may work well if the data are tapered. The theoretical results are verified by some simulated examples.