Linearality of Polynomial Models of Discrete Time Series
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.