Simulation of warping processes with applications to temperature data

TL;DR

This paper develops and compares three methods for simulating continuous warping processes with controlled mean and variance, crucial for functional data analysis, and demonstrates their application to temperature data analysis.

Contribution

Introduces a new randomized empirical CDF-based algorithm for simulating warping processes with theoretical guarantees and compares it with existing methods.

Findings

The new method effectively controls the mean and variance of simulated warping processes.

All three methods are validated through numerical simulations.

Application to temperature data illustrates practical utility.

Abstract

Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that properly account for phase variability in functional data. In this paper, we focus on the simulation of continuous warping processes with a prescribed expectation and a controllable variance. We study and compare three procedures, including two existing methods and a new algorithm based on randomized empirical cumulative distribution functions. For each approach, we provide an operational description and establish theoretical results for the first two moments of the simulated processes. A numerical study illustrates the theoretical findings and highlights the respective merits of the three methods. Finally, we present an application to the analysis of temperature distributions in Montreal based on simulated realizations from a warping process estimated from temperature quantile functions.