Electronic Proceedings of the Eighteenth Annual International Conference on Technology in Collegiate MathematicsOrlando, Florida, March 16-19, 2006Paper C032Using JavaScript to Study the Stability of Time-Varying ARMA Models |
Paul BouthellierDepartment of Mathematics and Computer Science University of Pittsburgh-Titusville Titusville, PA 16354 Phone: (814) 827-4432 Fax: (814) 827-5574 pbouthe@pitt.edu list of all papers by this author | Saeed DubasDepartment of Mathematics and Computer Science University of Pittsburgh-Titusville Titusville, PA 16354 Phone: (814) 827-5672 Fax: (814) 827-5574 dubasis@pitt.edu list of all papers by this author |
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ABSTRACT
In many mathematical modeling, differential equations, and numerical analysis classes, ARMA models are studied. In most cases however, the analysis is restricted to the time-invariant case.In this talk we will study how perturbations on the coefficients in the autoregressive (AR) part of the system affect the stability of the system. In particular, it will be shown that time-varying systems which are stable in frozen-time are not necessarily stable as time-varying systems.
A JavaScript program will allow simulations of time-varying ARMA models to be run. The affects of perturbations in the coefficients will be studied. The time-varying poles of the system, which are used to analyze the stability of such systems, are also computed by the program.
Keyword(s): modeling, differential equations