A consistent estimator of the smoothing operator in the functional Hodrick-Prescott filter

TL;DR

This paper introduces a functional Hodrick-Prescott filter for functional time series, demonstrating that the optimal smoothing operator maintains the noise-to-signal structure and providing a consistent estimator for it.

Contribution

The paper develops a consistent estimator for the optimal smoothing operator in the functional Hodrick-Prescott filter, enhancing its applicability to functional time series.

Findings

Optimal smoothing operator preserves noise-to-signal structure

Proposed estimator is consistent

Enhances functional time series analysis

Abstract

In this paper we consider a version of the functional Hodrick-Prescott filter for functional time series. We show that the associated optimal smoothing operator preserves the 'noise-to-signal' structure. Moreover, we propose a consistent estimator of this optimal smoothing operator.