# American Institute of Mathematical Sciences

2005, 2005(Special): 720-729. doi: 10.3934/proc.2005.2005.720

## Minimum degrees of polynomial models on time series

 1 Department of Mathematics, Morehouse College, Atlanta, GA 30314-0076, United States

Received  June 2004 Revised  March 2005 Published  September 2005

This paper studies polynomial models of time series. The focus will be on minimum degrees of polynomial modeling, in particular, the minimum degrees for arbitrary tail row. The paper proves decomposition theorems to reduce the associated matrices of time series to various matrix blocks. It introduces an augmented matrix of the associated matrix and gives a simple equivalent condition for existence of linear models. Moreover, it provides a new algorithm to get polynomial models, which improves the upper bound on the minimum degrees to $\le m-\bar l+1$ for an $m+1$ step time series with its augmented matrix of rank $\bar l$.
Citation: Chuang Peng. Minimum degrees of polynomial models on time series. Conference Publications, 2005, 2005 (Special) : 720-729. doi: 10.3934/proc.2005.2005.720
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