Parameter estimation of structural commodity price models

Commodity price modeling is normally approached in terms of structural time-series models, in which the different components (states) have a financial interpretation. The parameters of these models can be estimated using maximum likelihood. This approach results in a non-linear parameter estimation problem and thus a key issue is how to obtain reliable initial estimates. In this paper, we focus on the initial parameter estimation problem for the Schwartz-Smith two-factor model commonly used in asset valuation. We propose the use of a two-step method. The first step considers a univariate model based only on the spot price and uses a transfer function model to obtain initial estimates of the fundamental parameters. The second step uses the estimates obtained in the first step to initialize a re-parameterized state-space-innovations based estimator, which includes information related to future prices. The second step refines the estimates obtained in the first step and also gives estimates of the remaining parameters in the model. This paper is part tutorial in nature and gives an introduction to aspects of commodity price modeling and the associated parameter estimation problem.

Esprit Futur : Le Corbusier and José Oubrerie at Saint-Pierre De Firminy, Firminy-Vert, France, 1968–2006

What is the secret mesmerism that death possesses and under the operation of which a modern architect – strident, confident, resolute – becomes rueful, pessimistic, or melancholic?1 Five years before Le Corbusier’s death at sea in 1965, the architect reluctantly agreed to adopt the project for L’Église Saint-Pierre de Firminy in Firminy-Vert (1960–2006), following the death of its original architect, André Sive, from leukemia in 1958.2 Le Corbusier had already developed, in 1956, the plan for an enclave in the new “green” Firminy town, which included his youth and culture center and a stadium and swimming pool; the church and a “boîte à miracles” near the youth center were inserted into the plan in the ’60s. (Le Corbusier was also invited, in 1962, to produce another plan for three Unités d’Habitation outside Firminy-Vert.) The Saint-Pierre church should have been the zenith of the quartet (the largest urban concentration of works by Le Corbusier in Europe, and what the architect Henri Ciriani termed Le Corbusier’s “acropolis”3) but in the early course of the project, Le Corbusier would suffer the diocese’s serial objections to his vision for the church – not unlike the difficulties he experienced with Notre Dame du Haut at Ronchamp (1950–1954) and the resistance to his proposed monastery of Sainte-Marie de la Tourette (1957–1960). In 1964, the bishop of Saint-Étienne requested that Le Corbusier relocate the church to a new site, but Le Corbusier refused and the diocese subsequently withdrew from the project. (With neither the approval, funds, nor the participation of the bishop, by then the cardinal archbishop of Lyon, the first stone of the church was finally laid on the site in 1970.) Le Corbusier’s ambivalence toward the project, even prior to his quarrels with the bishop, reveals...