IJPAM: Volume 17, No. 2 (2004)

LINEAR TRANSFORMATIONS ON
POLYNOMIAL MODELS OF TIME SERIES

Aihua Li$^1$, Chuang Peng$^2$
$^1$Department of Mathematical Sciences
Montclair State University
1 Normal Avunue, New Jersey, 07043, USA
e-mail: ali@loyno.edu
$^2$Department of Mathematics
Morehouse College
830 Westview Drive, S.W. Atlanta, GA 30314, USA
e-mail: cpeng@morehouse.edu


Abstract.This paper studies polynomial modeling of time series. It introduces methods of using linear transformations to help construct polynomial models for an arbitary time series. It proves that a time series has linear models if the reduced column-echelon form of the associated matrix is diagonal, in particular, if it is of full rank. An upper bound for the minimum degree of all polynomial models is provided in case the reduced column-echolon form of the associated matrix is not diagonal. If the time series has $m+1$ time steps, then the minimal total degree of its polynomial models is less than or equal to $m+1-\rank(M)$, where $M$ is the associated matrix. As applications of the theorems, examples in various cases are investigeted.

Received: October 21, 2004

AMS Subject Classification: 39A10, 37N25

Key Words and Phrases: time series, polynomial model, linear model, linear transformation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 17
Issue: 2