By Terence C. Mills (auth.)

ISBN-10: 1137291265

ISBN-13: 9781137291264

ISBN-10: 1349350273

ISBN-13: 9781349350278

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

**Example text**

Page 31). 15]. The tentative answer to the problem of my title is therefore this: that some time-series are conjunct series with conjunct differences, and that when we take samples from two such series the distribution of correlations between them is U-shaped – we tend to get high positive or high negative correlations between the samples, without any regard to the true value of the correlation between the series that would be given by long experience over an indefinitely extended time. , page 39) Yule emphasized that conjunct series with random differences (the sum of a random series with zero mean) would swing above and below the zero base line but, as the length of the series was increased, would not tend to be correlated with time (viz.

19 Serial difference correlations for h = 5 (r 5 (k)) (dots) and a curve constructed from certain of the periodicities given by Beveridge (dashed line) terms t and t + k. The important matter in classification was the form of the function relating r(k) to k, which indicated the nature of the serial correlations between differences of the time series. If this function is linear, the time-series has random differences; if it gives a graph concave downwards the difference correlations are positive.

The result is in complete contrast with what we expect in sampling under the conditions usually assumed, when successive values of either variable drawn from the sample are independent of one another. In that case the values of r in successive samples may differ widely, but the mode tends to coincide with the ‘true’ value in the aggregate from which the sample is drawn – zero in the present illustration. Here the values in the samples tend to diverge as widely as possible, in both directions, from the truth.

### A Very British Affair: Six Britons and the Development of Time Series Analysis During the 20th Century by Terence C. Mills (auth.)

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