Journal of Time Series Analysis

ON LOW AND HIGH FREQUENCY ESTIMATION

Journal Article

Abstract. Estimating low or high frequencies is usually more difficult than estimating ordinary frequencies. In this paper, we show that the estimation accuracy depends on the combination of frequency, phase and sample size. For the best case, the mean square error can be smaller than the standard asymptotic Cramèr–Rao bound for an unbiased estimator in the Gaussian white noise case. Asymptotic theory for two limit procedures—the frequency changes as sample size increases or the frequency is fixed while the signal to noise ratio (SNR) increases—is established. Simulation shows that this theory is relevant for a wide range of situations which vary from small sample size (10) and high SNR (≥ 4) to large sample size (1000) and low SNR (≥ ‐16).

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