Principal Components and the Long Run
AbstractWe investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and densities, including densities without compact support and even densities with algebraic tails. We provide primitive sufficient conditions for the existence of these principal components. We also characterize the limiting behavior of the associated eigenvalues, the objects used to quantify the incremental importance of the principal components. By exploiting the theory of continuous-time, reversible Markov processes, we give a different interpretation of the principal components and the smoothness constraints. When the diffusion matrix is used to enforce smoothness, the principal components maximize long-run variation relative to the overall variation subject to orthogonality constraints. Moreover, the principal components behave as scalar autoregressions with heteroskedastic innovations. Finally, we explore implications for a more general class of stationary, multivariate diffusion processes.
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Bibliographic InfoPaper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000997.
Date of creation: 31 Dec 2005
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- Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004.
"Kernel-based nonlinear canonical analysis and time reversibility,"
Journal of Econometrics,
Elsevier, vol. 119(2), pages 323-353, April.
- Serge Darolles & Jean-Pierre Florens & Christian Gourieroux, 2000. "Kernel Based Nonlinear Canonical Analysis and Time Reversibility," Working Papers 2000-18, Centre de Recherche en Economie et Statistique.
- Serge Darolles & Jean-Pierre Florens & Christian Gourieroux, 1998.
"Kernel Based Nonlinear Canonical Analysis,"
98-55, Centre de Recherche en Economie et Statistique.
- Darolles, S. & Florens, J.-P. & Gourieroux, C., 1999. "Kernel Based Nonlinear Canonical Analysis," Papers 99.514, Toulouse - GREMAQ.
- Darolles, Serge & Florens, Jean-Pierre & Gouriéroux, Christian, 1999. "Kernel Based Nonlinear Canonical Analysis," IDEI Working Papers 83, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2001.
- Christian Bontemps & Nour Meddahi, 2012.
"Testing distributional assumptions: A GMM aproach,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 27(6), pages 978-1012, 09.
- Bontemps, Christian & Meddahi, Nour, 2007. "Testing Distributional Assumptions: A GMM Approach," IDEI Working Papers 486, Institut d'Économie Industrielle (IDEI), Toulouse.
- N. Meddahi & C. Bontemps, 2004. "Testing Distributional Assumptions: A GMM Approach," Econometric Society 2004 North American Winter Meetings 487, Econometric Society.
- Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004.
"Analytical Evaluation Of Volatility Forecasts,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
- MEDDAHI, Nour, 2001.
"An Eigenfunction Approach for Volatility Modeling,"
Cahiers de recherche
2001-29, Universite de Montreal, Departement de sciences economiques.
- Florens, Jean-Pierre & Renault, Eric & Touzi, Nizar, 1998. "Testing For Embeddability By Stationary Reversible Continuous-Time Markov Processes," Econometric Theory, Cambridge University Press, vol. 14(06), pages 744-769, December.
- Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
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