Principal components and the long run

Arbeitspapier

We 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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP07/09

Classification and Topics

• Classification: Wirtschaft
• Subject: Multivariate Analyse ; Markovscher Prozess ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Chen, Xiaohong ; Hansen, Lars Peter ; Scheinkman, José A.
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2009

Further information

• DOI: doi:10.1920/wp.cem.2009.0709
• Handle: http://hdl.handle.net/10419/64671
• Last update: 10.03.2025, 11:44 AM CET