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Identifying the finite dimensionality of curve time series

By Neil Bathia, Qiwei Yao and Flavio Ziegelmann

Abstract

The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence across different curves. The practical implementation of our method boils down to an eigenanalysis of a finite-dimensional matrix. Furthermore, the determination of the dimensionality is equivalent to the identification of the nonzero eigenvalues of the matrix, which we carry out in terms of some bootstrap tests. Asymptotic properties of the proposed method are investigated. In particular, our estimators for zero-eigenvalues enjoy the fast convergence rate n while the estimators for nonzero eigenvalues converge at the standard √n-rate. The proposed methodology is illustrated with both simulated and real data sets

Topics: QA Mathematics
Publisher: Institute of Mathematical Statistics
Year: 2010
DOI identifier: 10.1214/10-AOS819
OAI identifier: oai:eprints.lse.ac.uk:31709
Provided by: LSE Research Online

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