Herman Wold

Herman Ole Andreas Wold (December 25, 1908 - February 16, 1992) was a Swedish statistician known for his work in time series analysis and econometrics. Eponymous terms include the Wold decomposition and the Cramér-Wold theorem.

Life

Herman Wold was born in Skien, Southern Norway the youngest in a family of six brothers and sisters. In 1912 the family moved to Sweden and became Swedish citizens. Herman's father had a small fur and hide business.

In 1927 Wold enrolled at the University of Stockholm to study mathematics. It was an opportune time for Harald Cramér had been appointed Professor of Actuarial Mathematics and Mathematical Statistics. Wold would later write, "To belong to Cramér's first group of students was good luck, an advantage that simply cannot be exaggerated."

After graduating in 1930 Wold worked for an insurance company; he also did work on mortality data with Cramér and later designed a tariff for the insurance companies. He started work on a PhD on stochastic processes with Cramér as supervisor. Away from the thesis Wold and Cramér did some joint work, their best known result being the Cramér-Wold theorem (1936).

Wold's thesis, "A Study in the Analysis of Stationary Time Series," was an important contribution. The main result was the "Wold decomposition" by which a stationary series is expressed as a sum of a deterministic component and a stochastic component which can itself be expressed as an infinite moving average. Beyond this, the work brought together for the first time the work on individual processes by English statisticians, principally Udny Yule, and the theory of stationary stochastic processes created by Russian mathematicians, principally A. Y. Khinchin.

In 1938 a government committee appointed Wold to do an econometric study of consumer demand in Sweden. The results were published in 1940. In parallel, he worked on the theory of demand. His book "Demand Analysis" (1952) brought together his work on the theory of demand, the theory of stochastic processes, the theory of regression and his work on Swedish data.

In 1943-4, Trygve Haavelmo put forward his ideas on the simultaneous equations model and why it should be the basis for econometric research. Wold disagreed with the approach favoured by Haavelmo and the Cowles Commission and in the years 1945-65 wrote extensively on the recursive causal chain model he thought more appropriate.

At the end of his career Wold turned away from econometric modelling and developed multivariate techniques for what he called "soft" modelling. Some of these methods were developed by his student K. G. Jöreskog.

The story of Wold's academic appointments is briefly told. In 1942 he became professor of statistics at Uppsala University and he stayed there until 1970. He then moved to Gothenburg, retiring from there in 1975.

Writings by H. O. A. Wold

* "A Study in the Analysis of Stationary Time Series" (1938)
* "Statistical Estimation of Economic Relationships", in Econometrica, 1949
*"Demand Analysis: A Study in Econometrics," with Lars Juréen, 1952.
* "Causality and Econometrics", in Econometrica, 1954
* "Econometric model building : essays on the causal chain approach" (edited by Herman O.A. Wold). 1964
* " The fix-point approach to interdependent systems" (edited by Herman Wold). 1980
* "Systems under indirect observation : causality, structure, prediction"(edited by K.G. Jöreskog and H. Wold). 1982 There is an extensive bibliography published with the ET interview (below).

Autobiography

*J. Gani (ed) (1982) "The Making of Statisticians," New York: Springer-Verlag.This has a chapter in which Wold tells the story of his life.

* See the ET interview under External Links.

Discussion

*Svante Wold "Wold, Herman Ole Andreas";, pp. 213-4 in "Leading Personalities in Statistical Sciences from the Seventeenth Century to the Present," (ed. N. L. Johnson and S. Kotz) 1997. New York: Wiley. Originally published in "Encyclopedia of Statistical Science. "

External links

* [http://korora.econ.yale.edu/et/interview/wold.pdf ET Interviews: Professor H. O. A. Wold] on the [http://korora.econ.yale.edu/et/ Econometric Theory] page.

* [http://cepa.newschool.edu/het/profiles/wold.htm New School: Herman Wold, 1908-1992]

* [http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=44712 Mathematics Genealogy Project: Herman Wold]

"There is a photograph at"
* [http://www.york.ac.uk/depts/maths/histstat/people/wold.gifH. O. A. Wold] on the [http://www.york.ac.uk/depts/maths/histstat/people/welcome.htm Portraits of Statisticians] page.

"See also"
* [http://planetmath.org/encyclopedia/CramerWoldTheorem.html Cramér-Wold theorem]
* [http://www.xycoon.com/wolds_decomposition.htm Wold decomposition]