Semi-parametric estimation of shifts

TL;DR

This paper introduces a semi-parametric method using Fourier transforms to estimate translation shifts in functions, providing theoretical analysis and applying it to velocity curve forecasting.

Contribution

It develops an $M$-estimator framework for shift estimation in a semi-parametric setting, with convergence and asymptotic analysis, and demonstrates practical application in velocity forecasting.

Findings

Estimator converges under specified conditions

Asymptotic behavior characterized

Effective in velocity curve forecasting

Abstract

We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using $M$-estimators. Fourier transform enables to transform this statistical problem into a semi-parametric framework. We study the convergence of the estimator and provide its asymptotic behavior. Moreover, we use the method in the applied case of velocity curve forecasting.