By Terence C. Mills (auth.)
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Additional info for A Very British Affair: Six Britons and the Development of Time Series Analysis During the 20th Century
Pages 10–12; italics in original) Yule then considered the case of two sine curves for which the correlation over the whole period was not zero. 2. 7, and was described by Yule thus:4 (i)t remains U-shaped, but has become asymmetrical. 98221, and frequencies are much higher near the positive limit. 8. We could only conjecture, in such a case, that the true correlation was positive, if we had a number of samples available, and noted that those giving a positive correlation were to those giving a negative correlation as about 2 to 1.
Page 268) The recording apparatus is then left to itself, but unfortunately boys get into the room and start pelting the pendulum with peas, sometimes from one side and sometimes from the other. The motion is now affected, not by superposed fluctuations but by true disturbances, and the effect on the graph will be of an entirely different kind. The graph will remain surprisingly smooth, but amplitude and phase will vary continually. 10) where, once again, ρ is the amplitude of the sine wave and n is the period.
2 (scaled by the standard deviation of the original random series). These are given in the rightmost column and show that the end terms in the sample are the most variable, the central terms are the least variable, and the standard deviations are symmetrical about the centre of the sample. 2 Coefficients of the terms in the deviations from the mean of the sample, in a sample of 10 terms from a series with random differences a, b, c, . . d. 81 +1 product of their respective standard deviations.