City Research Online

Abstract

Much previous work (e.g. Durbin and Watson 1950, 1951, 1971) concerning autocorrelated errors associated with the general linear model has been based upon the assumption that the autocorrelation structure follows the stationary first-order Markov process. Here, by consideration of experimental designs in which correlations between errors seem likely, a non-stationary process is postulated.

First, a modification of the likelihood ratio produces a statistic, designated g , for testing the hypothesis of first order autocorrelation. This test is the most powerful invariant test against both non-stationary and stationary alternatives in the region of high autocorrelation. It is therefore more powerful than the Durbin-Watson test for these alternatives. Bounds are established for the g statistic under general conditions. In the ‘particular case where an overall mean is included in the regression the bounds are identical to those of the Durbin-Watson statistic.

An account is given of computer simulations for the purpose of examining the properties of various estimation procedures suggested in the literature and some new ones. A method based on a simple Bayesian decision approach, involving the g statistic, is shown to be reesonably efficient and is comparatively easy to use in practice.

Qualitative and quantitative design problems are discussed. Williams' (1949) changeover designs, in which every treatment follows every other treatment, are shown to minimize the generalized variance of estimates of parameters for randomized block and latin square designs, and for positive and negative first-order alternatives. This result is as yet without analytic proof. The theory of a design procedure is given for the general quantitative factor experiment and is critically compared with the method proposed by Box and Guttman (1966).

Finally an alternative to the von Neumann (1941) ratio, based on the g statistic, is developed for testing for the presence of autocorrelation in an observed sequence with zero mean.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science Q Science > QA Mathematics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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