Distribution of the Circular Serial Correlation Coefficient for Residuals from a Fitted Fourier Series
R. L. Anderson,T. W. Anderson +1 more
TLDR
In this article, the authors considered the observations are considered to be normally distributed with constant variance and means consisting of linear combinations of certain trigonometric functions, and 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 CSC coefficient for residuals from the fitted Fourier series.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).read more
Citations
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Journal ArticleDOI
Testing for serial correlation in least squares regression. II.
James Durbin,G. S. Watson +1 more
TL;DR: The problem of testing the errors for independence forms the subject of this paper and its successor and deals mainly with the theory on which the test is based, while the second paper describes the test procedures in detail and gives tables of bounds to the significance points of the test criterion adopted.
Journal ArticleDOI
The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator
Simo Puntanen,George P. H. Styan +1 more
TL;DR: In this paper, the development of the several conditions for the OLS estimator to be best linear unbiased is presented, in a historical perspective, using generalized inverses and orthogonal projectors.
Journal ArticleDOI
A set-based approach for white noise modeling
TL;DR: This paper provides a new framework for analyzing white noise disturbances in linear systems; rather than the usual stochastic approach, noise signals are described as elements in sets, and their effect is analyzed from a worst-case perspective.
References
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Degrees of freedom.
TL;DR: The article by Walker, H. W. as discussed by the authors was transcribed from the original by Chris Olsen, George Washington High School, Cedar Rapids, Iowa, who has made every attempt to reproduce the look and feel of the article as well as the article itself, and did not attempt in any way to update the symbols to more modern notation.
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On the theory of testing serial correlation
TL;DR: In this article, the Neyman-Pearson theory is applied to the problem of testing serial correlation in quadratic forms, and certain theorems concerning more general problems of Quadratic Form are developed and later applied to test serial correlation.