The Annals of Statistics

Identifying the finite dimensionality of curve time series

Neil Bathia, Qiwei Yao, and Flavio Ziegelmann

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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.

Article information

Ann. Statist. Volume 38, Number 6 (2010), 3352-3386.

First available in Project Euclid: 30 November 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 60G99: None of the above, but in this section

Autocovariance curve time series dimension reduction eigenanalysis Karhunen–Loéve expansion n convergence rate root-n convergence rate


Bathia, Neil; Yao, Qiwei; Ziegelmann, Flavio. Identifying the finite dimensionality of curve time series. Ann. Statist. 38 (2010), no. 6, 3352--3386. doi:10.1214/10-AOS819.

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