Early life
Herman Wold was born in Skien, Southern Norway. He was the youngest in a family of six brothers and sisters. In 1912 the family moved toScientific achievements
Herman Wold had a long and productive career, spanning six decades.Studying with Harald Cramér
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 theTime series and the Wold decomposition
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 process, 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 Aleksandr Yakovlevich Khinchin, A. Ya. Khinchin. Wold's results on univariate time series were generalized to multivariate time series by his student Peter Whittle (mathematician), Peter Whittle. The Wold decomposition and the related Wold's theorem inspired Arne Beurling, Beurling's Hardy space#Factorization, factorization theorem in Harmonic analysis#Abstract harmonic analysis, harmonic analysis and related work on invariant subspaces of linear operators.Theory of consumer demand
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 supply and demand, theory of demand. His book ''Demand Analysis'' (1952) brought together his work on the theory of demand, the theory of stochastic processes, the regression analysis, theory of regression and his work on Swedish data. * * * ) *Systems of simultaneous equations and causal inference
In 1943 and 1944, Trygve Haavelmo put forward his ideas on the Simultaneous equation methods (econometrics), simultaneous equations model, arguing that simultaneous equation methods (econometrics), systems of simultaneous equations should be central in econometric research. Wold noted some limitation of the maximum-likelihood approach favoured by Haavelmo and the Cowles Commission for Research in Economics, Cowles Commission; Wold cautioned that the literature contained some exaggerated claims for the superiority of maximum-likelihood estimation. In 1945 to 1965, 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 estimation theory, theoretical properties, which it lacked for general time-series models. Wold's writings on causality and recursive-chain models have been recognized as scientific inventions by recent work on causality and graphical models in statistics, especially by Judea Pearl and Nanny Wermuth.Multivariate analysis and partial least squares
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 through interactions with his student Karl Jöreskog, K. G. Jöreskog, although the latter's focus was primarily on maximum likelihood methods.Appointments
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.Selected writings by H. O. A. Wold
* 1938. ''A Study in the Analysis of Stationary Time Series'', Almqvist & Wiksell * 1949. ''Statistical Estimation of Economic Relationships'', in Econometrica, * 1952. ''Demand Analysis: A Study in Econometrics,'' with Lars Juréen. * 1954. "Causality and Econometrics," ''Econometrica'', 22(2),See also
* Causality * Harald Cramér, Cramér, Harald * Convex preferences *Notes
References
;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