Empirical Dynamic Material Flow Model for Tungsten in the USA

Multivariate polynomial regression (MPR) analysis was implemented to develop a nonlinear dynamic material flow model (DMFM) of tungsten in the United States for the years 1975–2000 without assumptions for lifetime distributions within reservoirs. Two external economic factors, the Consumer Price Index and the Industrial Production Index, were included as possible exogenous variables. Six types of vector time-series models were developed using multilinear, simple interaction, and MPR models, each with and without the exogenous economic variables. The DMFMs developed in this work make one-step-ahead predictions. That is, the material flows in a given year were predicted using flows and exogenous variables from previous years. In contrast to approaches that utilize assumed lifetime distributions for material within reservoirs, such as the Weibull distribution, the approach used here is completely data driven. MPR models produced statistically better results than linear models for all 13 flows that were modeled. Four of these models used simple interaction terms (which we call linear interaction terms), and two of these incorporated exogenous variables. The other nine models utilized higher-degree terms with interactions (called multivariate polynomial terms), and two of these incorporated exogenous variables. We conclude that nonlinear vector time series are capable of identifying complex relationships among material flows and exogenous variables. An understanding of these relationships has potential for managing, conserving, and/or forecasting the use of a resource.