Wavelet estimation of the dimensionality of curve time series

TL;DR

This paper introduces a wavelet-based method for estimating the dimensionality of curve time series, offering theoretical guarantees, computational efficiency, and practical validation through simulations and real data application.

Contribution

It proposes a novel wavelet representation approach to determine the finite-dimensional space of functional time series, improving on existing methods.

Findings

Method has strong asymptotic properties.

Wavelet representation enables fast algorithms.

Validated with simulations and real data.

Abstract

Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among other principles, have been used to tackle this issue. We discuss here a solution based on a finite-dimensional functional space. We employ wavelet representation of the functionals to estimate this finite dimension, and successfully model a time series of curves. The proposed method is shown to have nice asymptotic properties. Moreover, the wavelet representation permits the use of several bootstrap procedures, and it results in faster computing algorithms. Besides the theoretical and computational properties, some simulation studies and an application to real data are provided.