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March, 1950 Distribution of the Circular Serial Correlation Coefficient for Residuals from a Fitted Fourier Series
R. L. Anderson, T. W. Anderson
Ann. Math. Statist. 21(1): 59-81 (March, 1950). DOI: 10.1214/aoms/1177729886

Abstract

In this paper the observations are considered to be normally distributed with constant variance and means consisting of linear combinations of certain trigonometric functions. The likelihood ratio criterion for testing the independence of the observations against the alternatives of circular serial correlation of a given lag is found to be a function of the circular serial correlation coefficient for residuals from the fitted Fourier series (Section 4). The exact distribution (Section 5), the moments (Section 6), and approximate distributions (Section 7) are given for the cases of greatest interest. From these results significance levels have been found (Section 3). The use of these levels is indicated (Section 2), and an example of their use is given (Section 3).

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R. L. Anderson. T. W. Anderson. "Distribution of the Circular Serial Correlation Coefficient for Residuals from a Fitted Fourier Series." Ann. Math. Statist. 21 (1) 59 - 81, March, 1950. https://doi.org/10.1214/aoms/1177729886

Information

Published: March, 1950
First available in Project Euclid: 28 April 2007

zbMATH: 0037.08803
MathSciNet: MR34011
Digital Object Identifier: 10.1214/aoms/1177729886

Rights: Copyright © 1950 Institute of Mathematical Statistics

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Vol.21 • No. 1 • March, 1950
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