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Collineation --- Geometry, Affine --- 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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Line geometry. --- Geometry, Affine. --- Associative rings.

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"One of the first textbooks ever to explain polynomial rings and affine spaces Description of contents is simple, concrete and easier to understand so that readers have as less obstacles as possible Almost all results are proved when they are used or referred to, except for the knowledge of algebra or topology to be acquired in the undergraduate study At the end of each chapter, there are many problems attached, which the author hope to guide the readers to advance into this area of research"--

Polynomial rings --- Geometry, Affine --- Geometry, Algebraic