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
16). These oscillations in the serial correlations would be practically eliminated by setting the differencing interval to either 5 or 6, thus determining the next two choices for h. The two serial correlation plots are almost identical, having pronounced oscillations with a peak-to-peak period of around 18 years and a trough-to-trough period of about 14 years. Setting h = 11 shows a peak-to-peak period of around 14 years and a trough-to-trough period of 12 years. Yule’s final choice was h = 15, which produces many minor oscillations in the serial correlations.
UT , then xt = u1 + u2 + · · · + ut is a series with random differences (in the simulations T is set at 100). 10. 697 for A1 , B1 and C1 , respectively. , page 60). 8 20 30 40 50 60 70 80 90 100 Three random series of k and will cease to be valid for large values. , page 60; italics in original) Yule next considered the case when the differences are correlated such that 1 rx (k) is a linear function of k. This can be expressed as 1 rx (k) = 1 − αk since 1 rx (0) = 1. 9) j=1 To utilize this result, Yule constructed a series with correlated differences by taking the random series ut and cumulating 11-period Yule: Nonsense Correlations 37 moving sums, that is, by calculating t t st = uj , sj = ut + 2ut−1 + · · · +2ut−10 + ut−11 , xt = j=t−10 t = 11, .
5) which is the variance of x over the interval u ± h. 5). Yule focused attention on the case where the phase shift was a quarter of the period, α = n/4. 3. Now suppose we only observe data for a short interval of the whole period, say that enclosed between the two verticals aa, bb. This interval is so short that the segments of the two curves enclosed between aa and bb are very nearly straight lines, that for y rising and that for x falling, so that the correlation between the two variables within this interval will therefore be close to −1.
A Very British Affair: Six Britons and the Development of Time Series Analysis During the 20th Century by Terence C. Mills (auth.)