A Functional Hodrick Prescott Filter

TL;DR

This paper introduces a functional version of the Hodrick-Prescott filter tailored for infinite-dimensional Hilbert space data, providing a new approach for smoothing functional data with a detailed characterization of the optimal smoothing parameter.

Contribution

It develops a novel functional Hodrick-Prescott filter and characterizes the optimal smoothing parameter for Gaussian functional data, extending traditional methods to infinite-dimensional settings.

Findings

Introduces a functional Hodrick-Prescott filter for Hilbert space data.

Provides a characterization of the optimal smoothing parameter for Gaussian functional data.

Extends smoothing techniques to infinite-dimensional functional data.

Abstract

We propose a functional version of the Hodrick-Prescott filter for functional data which take values in an infinite dimensional separable Hilbert space. We further characterize the associated optimal smoothing parameter when the associated linear operator is compact and the underlying distribution of the data is Gaussian.