# Udny Yule

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

## Life

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

## Work

In addition to his famous and appeared in many editions textbook Introduction to the Theory of Statistics Yule has left a number of contributions that represent milestones in the development of statistics. He is considered one of the founders of applied correlation and regression analysis and has introduced so far generally accepted association measures. His most significant contributions he delivered in 1926/27 in the field of time series analysis.

Yule breakthrough idea of 1927 was to provide the " residual component " of a time series in the focus of interest. Until that time, was considered random noise in the time series as interfering components, the ones with a specific semantic content, superimposed the " real" components. Yule, however, came from a completely different idea. He wrote first a harmomische sine function in the form of a difference equation.

In this representation, which was completely identical without random effects with the functional representation, however, resulted in a fundamentally different role for the random variables. Yule described the behavior of such a disturbed series with a now famous analogy: The motion of a pendulum would be judged in equally spaced intervals, creating a pure trigonometric oscillation is described. These measurements are subject to errors due to imperfect measuring instruments, purely additive and independent of each other. But then passing the following:

If one could write a sine function in the form of a difference equation, the difference equation form other hand, was not limited to a particular shape. Yule therefore also examined models of the type mentioned with three instead of two time-shifted " regressors " and stressed that the number of these time-delayed variables is in principle not restricted. So one could consider such models of a very general form and determine their parameters by the least squares method. With this modeling, the so-called autoregressive processes (AR ( p) models) were newborn, who had A. Markow 1906/1911 derived from purely mathematical considerations. They were later removed together with "moving - average" models to a general theory of ARMA models and currently form one of the foundations of modern time series analysis. For Yule was given by the Royal Statistical Society awarded the golden medal Guy.

The Yule index from the text analysis is connected with his name.

## Important publications

- George Udny Yule: Why do we sometimes get nonsense correlations in 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.
- N. L. Johnson, S. Kotz: George Udny Yule. In: this. ( Eds. ), Leading personalities in statistical sciences, New York 1997, pp. 168-169.