An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windows

TL;DR

This paper introduces an auto-regressive approach to time-series smoothing that enhances smoothing quality while maintaining efficiency, resulting in moving means with exponentially tapered windows.

Contribution

It presents a novel auto-regressive formulation for smoothing, linking it to exponentially tapered moving mean windows, and demonstrates its efficiency and improved smoothing capabilities.

Findings

Auto-regressive smoothers enforce higher smoothing levels.

Auto-regressive models are as efficient as traditional moving means.

Resulting moving means have exponentially tapered windows.

Abstract

We investigate an auto-regressive formulation for the problem of smoothing time-series by manipulating the inherent objective function of the traditional moving mean smoothers. Not only the auto-regressive smoothers enforce a higher degree of smoothing, they are just as efficient as the traditional moving means and can be optimized accordingly with respect to the input dataset. Interestingly, the auto-regressive models result in moving means with exponentially tapered windows.