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Identifying the finite dimensionality of curve time series

Bathia, Neil, Yao, Qiwei ORCID: 0000-0003-2065-8486 and Ziegelmann, Flavio (2010) Identifying the finite dimensionality of curve time series. Annals of Statistics, 38 (6). pp. 3352-3386. ISSN 0090-5364

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Identification Number: 10.1214/10-AOS819


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.

Item Type: Article
Official URL:
Additional Information: © 2010 Institute of Mathematical Statistics
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 26 Jan 2011 09:48
Last Modified: 16 May 2024 01:05

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