Journal of Time Series Analysis


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).

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.