George Udny Yule

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George Udny Yule (born February 18, 1871 in Morham , Scotland , † June 26, 1951 in Cambridge , England ) was a Scottish statistician .


Yule came from a family of Scottish officers, civil servants and scholars, first studied engineering in London and then devoted a year in Bonn to studying electrical waves with Heinrich Hertz . In 1893 he returned to London and was offered a position at University College London by Karl Pearson , whom Yule had met as a student ; then he became an assistant professor there . Between 1902 and 1909 he held, again at University College, the Newmarch Lectureship in Statistics at the Faculty of Agricultural Sciences. In 1912 he became lecturer for statistics at Cambridge University , where he taught until 1940 , apart from activities for the War Office and the Ministry of Food between 1915 and 1919.


In addition to his famous and widely-published textbook Introduction to the Theory of Statistics , Yule has left a number of articles that represent milestones in the development of statistics. He is considered to be one of the founders of applied correlation and regression analysis and has introduced generally recognized association measures to this day. He made his most important contributions in 1926/27 in the field of time series analysis .

Yule's groundbreaking idea from 1927 was to put the “residual component” of a time series at the center of interest. Up until this point in time, random disruptions in time series were viewed as disruptive components that superimposed the “actual” components, those with a specific meaning. Yule, on the other hand, assumed a completely different idea. To this end, he first wrote a harmonic sine function in the form of a difference equation.

In this representation, which was completely identical to the functional representation without any random influences, there was, however, a fundamentally different role for the random variables. Yule described the behavior of such a disturbed series with a now famous analogy: The movement of a pendulum is measured at equidistant intervals, which describes a pure trigonometric oscillation. These measurements are flawed by imperfect measuring instruments, are purely additive and independent of one another. But then the following happens:

The recording apparatus is left to itself, and 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.

On the other hand, if a sine function could be written in the form of a difference equation, the difference equation form was not limited to a particular form. Yule therefore also examined models of the type mentioned with three instead of two time-shifted “regressors” and emphasized that the number of these time-shifted variables is in principle not limited. Such models can be viewed in a very general form and their parameters can be determined using the least squares method. With this modeling, the so-called autoregressive processes (AR (p) models) were reborn, which A. Markow had derived in 1906/1911 from purely mathematical considerations. They were later expanded to form a general theory of ARMA models together with “moving average” models and currently form one of the foundations of modern time series analysis. For this, Yule was awarded the golden Guy Medal by the Royal Statistical Society .

The Yules Index from Text Analysis is associated with his name.

Important publications

  • George Udny Yule: Why do we sometimes get nonsense correlations between time-series? A study in sampling and the nature of time series (with discussion) . In: Journal of the Royal Statistical Society, No. 89, 1926, pp. 1-69. Reprinted (without discussion) in Stuart / Kendall (1971)
  • George Udny Yule: On a method of investigating periodicities in disturbed series, with special reference to Wolfer's sunspot numbers . In: Philosophical Transactions of the Royal Society of London A, No. 226, 1927, pp. 267-298. Reprinted in Stuart / Kendall (1971)

further reading

  • Alan Stuart, Maurice G. Kendall (Eds.): Statistical papers of George Udny Yule . Hafner Pub. Co., New York 1971.
  • F. Yates: George Udny Yule. In: Obituary Notices of Fellows of the Royal Society of London 8 (1952), pp. 309-323.
  • NL Johnson, S. Kotz : George Udny Yule . In this. (Eds.), Leading personalities in statistical sciences , New York 1997, pp. 168-169.

See also

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