By Terence C. Mills (auth.)
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Extra info for A Very British Affair: Six Britons and the Development of Time Series Analysis During the 20th Century
If this function is linear, the time-series has random differences; if it gives a graph concave downwards the difference correlations are positive. We concluded that it was series of the latter type (positively correlated series with positively correlated differences, or conjunct series with conjunct differences to use my suggested term) that formed the dangerous class of series, correlations between short samples tending towards unity. Experimental investigation completely confirmed this suggestion.
Page 14) The phenomenon is clearly related to the fact that a small segment of a sine curve, when taken at random, will usually be either rising or falling and so will tend to be highly correlated (of either sign) with other segments taken at random. 99985 gives the correlation between the value of the variable in one year and the value in the next. 98481. , page 14). With this concept thus defined, Yule then considered answering the following question: will it suffice to give us a U-shaped distribution of correlations for samples from two empirical series, if the serial correlations for both of them are high, and positive at least as far as rx (T − 1) where T is the number of terms in the sample?
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.
A Very British Affair: Six Britons and the Development of Time Series Analysis During the 20th Century by Terence C. Mills (auth.)