Principal Components and Long Run Implications of Multivariate Diffusions
Principal Components and Long Run Implications of Multivariate Diffusions
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多元扩散的主成分和长期影响
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J. Scheinkman
中科院分区：
文献类型：
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作者：
Xiaohong Chen;L. Hansen;J. Scheinkman
研究了一种非线性主成分的提取方法。这些主成分最大化的变化受到平滑性和正交性约束，但我们允许一般类的约束和多变量密度，包括密度没有紧支持，甚至密度代数尾。我们提供原始的充分条件，这些主成分的存在。我们描述了相关特征值的限制行为，这些特征值是用于量化主成分的增量重要性的对象。通过利用连续时间，可逆马尔可夫过程的理论，我们给出了不同的解释的主成分和光滑性约束。当使用扩散矩阵来增强平滑度时，主成分相对于受正交性约束的总体变化最大化长期变化。此外，主成分表现为标量自回归与异方差创新，这支持半参数识别的多变量可逆扩散过程和测试的overidentifying的限制，这样一个过程中隐含的低频数据。我们还探讨了固定的，可能是不可逆的扩散过程的影响。
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 multivariate 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 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; this supports semiparametric identification of a multivariate reversible diffusion process and tests of the overidentifying restrictions implied by such a process from low frequency data. We also explore implications for stationary, possibly non-reversible diffusion processes.
影响因子：
2.7
作者：
Zhou, Lan;Huang, Jianhua Z.;Carroll, Raymond J.
通讯作者：
Carroll, Raymond J.