Noise reduction for functional time series

TL;DR

This paper introduces a new noise reduction method for functional time series using an extension of FPCA, which effectively separates signal from noise, leading to improved denoising and forecasting accuracy.

Contribution

The paper develops a novel FPCA-based approach for noise reduction in functional time series, demonstrating its consistency and superiority over existing methods.

Findings

The method effectively denoises simulated and real data.

It outperforms existing noise reduction techniques.

It enhances forecasting accuracy when used as preprocessing.

Abstract

A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional dynamics of the functional time series to separate the serially dependent dynamical part of the observed curves from the noise. Upon identifying the subspaces of the signal and idiosyncratic components, we construct a projection of the observed curve time series along the noise subspace, resulting in an estimate of the underlying denoised curves. This projection is optimal in the sense that it minimizes the mean integrated squared error. By applying our method to similated and real data, we show the denoising estimator is consistent and outperforms existing denoising techniques. Furthermore, we show it can be used as a pre-processing step to improve forecasting.