ESTIMATING FREQUENCY BY INTERPOLATION USING FOURIER COEFFICIENTS

The periodogram of a time series that contains a sinusoidal component provides a crude estimate of its frequency parameter, the maximizer ov er the Fourier frequencies being within O(T-1) of the frequency as the sample size T increases. In this correspondence, a technique for obta ining an estimator that has root mean square error of order T-3/2 is p resented, which involves only the Fourier components of the time serie s at three frequencies. The asymptotic variance of the estimator varie s between, roughly, the asymptotic variance of the maximizer of the pe riodogram over all frequencies (the Cramer-Rao lower bound) and three times this variance. The advantage of the new estimator is its computa tional simplicity.