Download A Very British Affair: Six Britons and the Development of by Terence C. Mills (auth.) PDF

By Terence C. Mills (auth.)

ISBN-10: 1137291265

ISBN-13: 9781137291264

ISBN-10: 1349350273

ISBN-13: 9781349350278

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Additional resources for A Very British Affair: Six Britons and the Development of Time Series Analysis During the 20th Century

Example text

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.

The full discussion of the mathematical problem – given two series, each with specified serial correlations, required to determine the frequency distribution of correlations between samples of T consecutive observations – I must leave to more competent hands. It is quite beyond my abilities, but I hope that some mathematician will take it up. The results that he may obtain may seem to be of mere theoretical importance, for in general we only have the sample itself, which may Yule: Nonsense Correlations 43 be quite inadequate for obtaining the serial correlations.

Interestingly, Yule ended the theoretical part of his paper with this statement: I give my answer to the problem as a tentative answer only, for I quite recognize that the discussion is inadequate and incomplete. The full discussion of the mathematical problem – given two series, each with specified serial correlations, required to determine the frequency distribution of correlations between samples of T consecutive observations – I must leave to more competent hands. It is quite beyond my abilities, but I hope that some mathematician will take it up.

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