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Correlation In Time Series Regression

The Geary Test

University of Akron

Sociologists have recently become more interested in testing dynamic models of social change via time series regression techniques (e.g., Snyder, 1975; Franke and Kaul, 1978; Burstein and Freudenburg, 1978). The existence of serial correlation in the disturbance term, which would constitute a violation of one of the standard regression model assumptions, is usually tested for in such models via the Durbm-Watson (1950, 1951) d test statrstic. However, the Durbin-Watson test often allows no inference concerning the existence of serial correlation because the critical values of the test cannot be tabulated exactly. Geary 1970 proposed a test statistic, tau, which is easy to calculate and has an exact probability distribution. This article discusses serial correlation and its consequences for OLS regression equations, proposes the Geary test as a convenient addition to the Durbin-Watson test, and argues that the Geary test provides additional information, especially in the case of indeterminancy in the Durbin-Watson. The use of tau is illustrated by replications of three sociological studies and, although the Geary test is consistently less powerful than the Durbin-Watson test, it is a useful additional piece of information in most situations.

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