| Principal Components and the Long Run (2007) | |||||||||||||||
Abstract | |||||||||||||||
| In this paper we suggest a method for extracting nonlinear principal components from the stationary distribution of a multivariate reversible diusion process. These principal components a) maximize variation subject to smoothness and orthogonality constraints; and b) maximize long-run variation subject to overall variation and orthogonality constraints. Moreover, the principal components behave as scalar autoregressions with heteroskedastic innovations. This link between the stationary distribution, the long run dynamics and the transient dynamics supports parametric and semiparametric identi cation of a diusion process and tests of the overidentifying restrictions implied by such a process. We provide sucient conditions for the existence of principal components for diusion processes with unbounded supports, and we study the limiting behavior of the corresponding eigenvalues. 1 | |||||||||||||||
Details der Publikation | |||||||||||||||
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