Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms

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The relationship between the ratio of the mean square successive difference to the variance and the serial or autocorrelation coefficient for an infinite series is given byr1= 1 – 1/2 δ2/s2wherer1is the first autocorrelation. It can be seen that asr1moves from +1 to −1 the ratio δ/s2moves from 0 to 4

The actual residuals were not published in the paper by Richard Stone but he has very kindly let us have the calculated residuals for 17 equations which include some revised estimates and a few additional relationships (see Table VIII)

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