The Best Linear Unbiased Estimator for Continuation of a Function

TL;DR

This paper develops an efficient method to construct the best linear unbiased predictor for continuing a curve modeled by splines, assuming the entire curve is a realization of a smooth stochastic process, with applications to call center data.

Contribution

It introduces a novel approach to compute the BLUP for function continuation in spline models, including confidence bands, with practical application to real-world data.

Findings

Efficient computation of BLUP for curve continuation.

Successful application to call center workload forecasting.

Demonstrated accuracy of predictions with real data.

Abstract

We show how to construct the best linear unbiased predictor (BLUP) for the continuation of a curve in a spline-function model. We assume that the entire curve is drawn from some smooth random process and that the curve is given up to some cut point. We demonstrate how to compute the BLUP efficiently. Confidence bands for the BLUP are discussed. Finally, we apply the proposed BLUP to real-world call center data. Specifically, we forecast the continuation of both the call arrival counts and the workload process at the call center of a commercial bank.