Yule and Hooker and the Concepts of Correlation and Trend

2.1 The foundations of modern time series analysis began to be laid in the late nineteenth century and were made possible by the invention of regression and the related concept of the correlation coefficient. By the final years of the century the method of correlation had made its impact felt primarily in biology, through the work of Francis Galton on heredity (Galton, 1888, 1890) and of Karl Pearson on evolution (Pearson 1896; Pearson and Filon, 1898).1 Correlation had also been used by Edgeworth (1893, 1894) to investigate social phenomena and by G. Udny Yule in the field of economic statistics, particularly to examine the relationship between welfare and poverty (Yule, 1895, 1896).2 This led Yule (1897a, 1897b) to provide a full development of the theory of correlation which, unusually from a modern perspective — but, as we shall see, importantly for time series analysis —, was based on the related idea of a regression between two variables X and Y.3 It also did not rely on the assumption that the two variables were jointly normally distributed, which was central to the formal development of correlation in Edgeworth (1892) and Pearson (1896). This was an important generalization, for Yule was quick to appreciate that much of the data appearing in the biological and social sciences were anything but normally distributed, typically being highly skewed.