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Collineation --- Geometry, Affine

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This paper characterizes, interprets, and tests the over-identifying restrictions imposed in affine models of the term" structure. Letting r(t) = ë Y(t), where Y is an unobserved vector affine process, our analysis proceeds in three steps. First, we show that affine models can be categorized according to the different over-identifying restrictions they impose on (i) ë, and (ii) the parameters of the diffusion matrices. Second, this formulation is shown to be equivalent to a model in which there is a terraced drift structure with one of the state variables being the stochastic long-run mean of r. This equivalence allows direct comparisons of the substantive restrictions on the dynamics of interest rates imposed in CIR-style models and models in which the state variables are the stochastic long-run mean and volatility of r. Third, we compute simulated method of moments estimates of a three-factor affine term structure model, and test the over-identifying restrictions on the joint distribution of long- and short-term interest rates implied by extant affine models of r. We find allowing for correlated factors is key to simultaneously describing the short and long ends of the yield curve. This finding is interpreted in terms of the properties of the risk factors underlying term structure movements.

Geometry, Affine. --- Econometric models.

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Vector spaces. --- Geometry, Affine. --- Collineation.

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Functions, Orthogonal --- Geometry, Affine --- Space and time

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Linear algebra is now included in the undergraduate curriculum of most universities. It is generally recognized that this branch of algebra, being less abstract and directly motivated by geometry, is easier to understand than some other branches and that because of the wide applications it should be taught as soon as possible. This book is an extension of the lecture notes for a course in algebra and geometry for first-year undergraduates of mathematics and physical sciences.

Geometry, Projective. --- Geometry, Affine. --- Algebras, Linear.