# Linearality of Polynomial Models of Discrete Time Series

## Document Type

Conference Proceeding

## Publication Date

12-1-2005

## Abstract

Consider a time series T and the set of polynomial models of T. We discuss two types of linearalities of T. The first type is measured by the maximal number of linear members of a polynomial model may have, denoted LN(T). An upper bound for LN(T) is given. The other is measured by the number of linear elements in a Gröbner Basis G of the ideal vanishing at all points of T, denoted LIN(G). Note that for each selected term order on the monomials of F[x1, ..., xn], there is a unique generating set, called the reduced Gröbner Basis, for the vanishing ideal mentioned above. We give a method to find linear members in G with respect to any term order. When selecting a graded term order (total degree prefered), we give a formula for the cardinality of LIN(G). Sample models are illustrated to support the theorems and propositions and they are constructed using the Buchberger Möller Algorithm.

## MSU Digital Commons Citation

Li, Aihua and Saydam, Serpil, "Linearality of Polynomial Models of Discrete Time Series" (2005). *Department of Mathematics Facuty Scholarship and Creative Works*. 101.

https://digitalcommons.montclair.edu/mathsci-facpubs/101