Times Series Methods for Modeling and Simulations of Terrain Profiles
Jinfeng Wei, T. C. Sun

Abstract
In this paper time series methods are used to model two terrain profiles obtained by the US Army at the Aberdeen Proving Grounds, Maryland and the Yuma Test Facility, Arizona. One profile has nonstationary behavior but has a linear structure. We can model it quite well by using the uniformly modulated processes introduced by Priestley. The other profile is also nonstationary but has a nonlinear structure. We model it with 3 different methods: ARMA-GARCH, TAR and EMD methods of which the EMD method may not be familiar to most statisticians. They all seem to fit it well. We use the linear damage theory in mechanics to make a more appealing fitness check of the 3 methods. We believe the experience we gained in this study may provide some insight into other nonstationary and nonlinear time series model builders.

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