Identifying the finite dimensionality of curve time series

TL;DR

This paper introduces a new eigenanalysis-based method to determine the dimensionality of curve time series, effectively handling nonstationary features and supported by bootstrap tests and asymptotic analysis.

Contribution

The paper presents a novel eigenanalysis approach for identifying the dimension of curve time series, with bootstrap testing and proven asymptotic properties.

Findings

Method accurately identifies dimensionality in simulations.

Estimators for zero eigenvalues converge at rate n.

Method effectively applied to real data.

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 $\sqrt{n}$-rate. The proposed methodology is illustrated with both simulated and real data sets.