Open Access
Translator Disclaimer
December 2010 Identifying the finite dimensionality of curve time series
Neil Bathia, Qiwei Yao, Flavio Ziegelmann
Ann. Statist. 38(6): 3352-3386 (December 2010). DOI: 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.


Download Citation

Neil Bathia. Qiwei Yao. Flavio Ziegelmann. "Identifying the finite dimensionality of curve time series." Ann. Statist. 38 (6) 3352 - 3386, December 2010.


Published: December 2010
First available in Project Euclid: 30 November 2010

zbMATH: 1204.62152
MathSciNet: MR2766855
Digital Object Identifier: 10.1214/10-AOS819

Primary: 62H30 , 62M10
Secondary: 60G99

Keywords: autocovariance , curve time series , Dimension reduction , eigenanalysis , Karhunen–Loéve expansion , n convergence rate , root-n convergence rate

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 6 • December 2010
Back to Top