A law of the iterated logarithm for an estimate of frequency

• Published in: Stochastic processes and their applications Vol. 22; no. 1; pp. 103 - 109
• Main Authors: Hannan, E.J., Mackisack, M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.1986; Elsevier Science; Elsevier
• Series: Stochastic Processes and their Applications
• Subjects: Exact sciences and technology; integrated logarithm; integrated logarithm oscillatory frequency periodogram weak mixing; Limit theorems; Mathematics; oscillatory frequency; periodogram; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; weak mixing; periodogram; weak mixing; integrated logarithm; oscillatory frequency; Stochastic convergence; Law of iterated logarithm
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/0304-4149(86)90117-1

A form of the law of the iterated logarithm is proved for the estimate of the frequency, ω 0, of a sinusoidal oscillation when observed subject to stationary noise. The estimate, ω , is the location of the maximum of the periodogram from T observations. The form of the law is unusual since it is { T 3 log log T } 1/2 ( ω−ω 0 whose limit superior is a.s. finite.