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 over the Fourier frequencies being within 0(T^-l) of the frequency as the sample size T increases. In this correspondence, a technique for obtaining an estimator that has root mean square error of order T^-3/2 is presented, which involves only the Fourier components of the time series at three frequencies. The asymptotic variance of the estimator varies between, roughly, the asymptotic variance of the maximizer of the periodogram over all frequencies (the Cramer-Rao lower bound) and three times this variance. The advantage of the new estimator is its computational simplicity.