| During his brief period of active participation in the work of the Cowles
Commission, Herbert Jones made a number of significant contributions to statistical and
econometric science. Trained in electrical engineering and equipped with an excellent
understanding of fundamental mathematics, he brought to bear upon the problems of the
Commission a keen and analytical point of view. His breadth of interest is readily
observed from the variety and difficulty of the studies which he made. His first
contribution was in the field of engineering economics, where the cost functions
associated with hydraulic pumping were analyzed. From this he turned to the study of the
statistics of time series, where new techniques were called for, and where analytical
leads were obscured by many difficult considerations.
He began his work by exploring the nature of regression functions in correlation
analysis and seized upon the concept of statistical hysteresis as a fruitful lead. He
differentiated between "tag hysteresis," which depends primarily upon sinusoidal
characteristics in the series, and "skew" hysteresis, which depends upon a lack
of symmetry in the cycles of the component series. His principle contribution was that the
"tag hysteresis" could be corrected for by serial correlation, but that
"skew hysteresis" could not be so corrected. Closely associated with this
problem was that of the nature of regression lines obtained by minimizing squared
residuals taken in directions other than those parallel to two perpendicular axes.
The properties of runs in economic time series intrigued his fancy and he devoted much
thought to this problem. He established frequency functions for such runs as they are
observed in various types of series, and in a joint paper with Alfred Cowles be applied
these findings to stock price movements. This paper has furnished us with a very important
example of the application of an abstract theory to actual economic data.
One clue to the analysis of economic time series is found in the concept of a random
series. The work of Herbert Jones in this field was of the highest character. He extended
some of the important results of Yule, and by a clever device replaced random sequences by
certain analytical functions which possessed identical properties.
His last investigation was a collaborative study with Forrest Danson on problems
associated with tax-exemption laws. This was published as a leading article in Barron's in
1939.
In all of these studies Herbert Jones proved himself to be a young man with an
exceptional imagination and an analytical power far beyond the average. Perhaps there is
no higher encomium possible than to repeat what was said about the remarkable English
mathematician, W.K. Clifford, who died very young: "If he had lived we might have
known something." |