Input estimation from discrete workload observations in a L\'evy-driven storage system

TL;DR

This paper develops a method to estimate the input process's characteristic exponent in a Lévy-driven storage system using workload observations, providing consistency, asymptotic normality, and improved resampling techniques.

Contribution

It introduces a novel estimator based on moment equations and Laplace transforms, with proven consistency and asymptotic properties, plus a resampling scheme for efficiency.

Findings

Estimator is pointwise consistent for any observation grid.

High frequency sampling yields asymptotically normal errors.

Resampling scheme improves estimation efficiency.

Abstract

Our goal is to estimate the characteristic exponent of the input to a L\'evy-driven storage system from a sample of equispaced workload observations. The estimator relies on an approximate moment equation associated with the Laplace-Stieltjes transform of the workload at exponentially distributed sampling times. The estimator is pointwise consistent for any observation grid. Moreover, a high frequency sampling scheme yields asymptotically normal estimation errors for a class of input processes. A resampling scheme that uses the available information in a more efficient manner is suggested and assessed via simulation experiments.