Herman Wold  

Born 
December 25, 1908 
Died 
February 16, 1992 (aged 83) 
Nationality  Swedish 
Institutions  Uppsala University 
Alma mater  University of Stockholm 
Doctoral advisor  Harald Cramér 
Doctoral students  Peter Whittle Karl Jöreskog 
Herman Ole Andreas Wold (December 25, 1908  February 16, 1992) was a Swedish statistician known for his work in time series analysis and econometrics, and for developing the methods of partial least squares regression and partial least squares path modeling. Eponymous terms include the Wold decomposition and the CramérWold theorem.
Contents 
Herman Wold had a long and productive career, spanning six decades.
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 CramérWold 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. The Wold decomposition inspired Beurling's factorization theorem in harmonic analysis and related work on invariant subspaces of linear operators. Wold's results on univariate time series were generalized to multivariate time series by his student Peter Whittle.
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 19434, Trygve Haavelmo put forward his ideas on the simultaneous equations model, arguing that systems of simultaneous equations should be central in econometric research. Wold noted some limitation of the maximumlikelihood approach favoured by Haavelmo and the Cowles Commission; Wold cautioned that the literature contained some exaggerated claims for the superiority of maximumlikelihood estimation.
In the years 194565, Wold proposed and elaborated on his "recursive causal chain" model, which was more appropriate for many applications, according to Wold: For such "recursive causal chain" models, the least squares method was computationally efficient and enjoyed superior theoretical properties, which it lacked for general timeseries models. Wold's writings on causality and chainmodels have been recognized as scientific inventions by recent work on causality and graphical models in statistics, especially by Judea Pearl and Nanny Wermuth.
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.
In 1960 Wold became a member of the Royal Swedish Academy of Sciences. He was a member of the Prize Committee for the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel from 1968 to 1980.
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.
There is an extensive bibliography published with the ET interview (below).
This has a chapter in which Wold tells the story of his life.
There is a photograph at
See also (external links, again)
