Parametric Covariance Models for Shock - induced Stochastic Processes

A common assumption in the modeling of stochastic processes is that of weak stationarity. Although this is a convenient and sometimes justifiable assumption for many applications, there are other applications for which it is clearly inappropriate. One such application occurs when the process is driven by action at a limited number of sites, or point sources. Interest may lie not only in predicting the process, but also in assessing the effect of the point sources. In this article we present a general parametric approach of accounting for the effect of point sources in the covariance model of a stochastic process, and we discuss properties of a particular family from this general class. A simulation study demonstrates the performance of parameter estimation using this model, and the predictive ability of this model is shown to be better than some commonly used modeling approaches. Application to a dataset of electromagnetism measurements in a field containing a metal pole shows the advantages of our parametric nonstationary covariance models. AMS classification: primary 62M30j secondary 60G12, 62M20