Estimating the Current Mean of a Process Subject to Abrupt Changes

Abstract

This article discusses estimation of the current process mean in situations in which this parameter is subject to abrupt changes of unpredictable magnitude at some unknown points in time. It introduces performance criteria for this estimation problem and discusses in detail the relative merits of several estimation procedures. I show that an estimate based on exponentially weighted moving average of past observations has optimality properties within the class of linear estimators, and I propose alternative estimating procedures to overcome its limitations. I consider two primary types of estimation procedures, Markovian estimators, in which the current estimate is obtained as a function of the previous estimate and the most current data point, and adaptive estimators, based on identification of the most recent changepoint. We give several examples that illustrate the use of the proposed techniques.