Identifying the finite dimensionality of curve time series

By N. Bathia, Qiwei Yao, Flávio Augusto Ziegelmann. 2010

86 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/bf0b678b5b06075c67382efd2b9af329e0f467e6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Clifford Lam
2. Han Lin Shang
3. Degui Li
4. Peter M. Robinson
5. Qiwei Yao

In Statistical and Nonlinear Physics

1. Han Lin Shang
2. Clifford Lam
3. Qiwei Yao

In Signal Processing

1. Han Lin Shang
2. Clifford Lam
3. Peter M. Robinson
4. Qiwei Yao

Citations in the corpus

• A survey of functional principal component analysis (2014, methodology): “There are numerous ways of determining the optimal number of K, such as the bootstrap approach proposed by Hall & Vial (2006) and Bathia et al. (2010), description length approach proposed by Poskitt & Sengarapillai (2013), pseudo-AIC (Shibata 1981), scree plot (Cattell 1966), and eigenvector variab”
• Long-Range Dependent Curve Time Series (2020, background): “…time series structures have been studied: one extends probabilistic and statistical tools developed for mixing sequences (Ferraty and Vieu 2006; Bathia, Yao, and Ziegelmann 2010); the other extends certain linear and nonlinear sequences and martingale or m-dependent approximation techniques…”
• Factor modeling for high-dimensional time series: inference for the number of factors (2012, methodology): “The proof of the above proposition is in principle the same as that of Theorem 1 in [4], and is therefore omitted.”