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
[1]

Yu-Ting Lin, John Malik, Hau-Tieng Wu. Wave-shape oscillatory model for nonstationary periodic time series analysis. Foundations of Data Science, 2021, 3 (2) : 99-131. doi: 10.3934/fods.2021009

[2]

David Schley, S.A. Gourley. Linear and nonlinear stability in a diffusional ecotoxicological model with time delays. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 575-590. doi: 10.3934/dcdsb.2002.2.575

[3]

Amir Mohammad Fakoor Saghih, Azam Modares. A new dynamic model to optimize the reliability of the series-parallel systems under warm standby components. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021189

[4]

G. Gentile, V. Mastropietro. Convergence of Lindstedt series for the non linear wave equation. Communications on Pure & Applied Analysis, 2004, 3 (3) : 509-514. doi: 10.3934/cpaa.2004.3.509

[5]

Ruiqi Li, Yifan Chen, Xiang Zhao, Yanli Hu, Weidong Xiao. Time series based urban air quality predication. Big Data & Information Analytics, 2016, 1 (2&3) : 171-183. doi: 10.3934/bdia.2016003

[6]

A. Pedas, G. Vainikko. Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 395-413. doi: 10.3934/cpaa.2006.5.395

[7]

Bernard Ducomet, Šárka Nečasová. Thermalization time in a model of neutron star. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 801-818. doi: 10.3934/dcdsb.2011.16.801

[8]

Simone Göttlich, Elisa Iacomini, Thomas Jung. Properties of the LWR model with time delay. Networks & Heterogeneous Media, 2021, 16 (1) : 31-47. doi: 10.3934/nhm.2020032

[9]

Shaoyong Lai, Qichang Xie. A selection problem for a constrained linear regression model. Journal of Industrial & Management Optimization, 2008, 4 (4) : 757-766. doi: 10.3934/jimo.2008.4.757

[10]

Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670-677. doi: 10.3934/proc.2015.0670

[11]

Joost Hulshof, Robert Nolet, Georg Prokert. Existence and linear stability of solutions of the ballistic VSC model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 35-51. doi: 10.3934/dcdss.2014.7.35

[12]

Fang Qin, Ying Jiang, Ping Gu. Three-dimensional computer simulation of twill woven fabric by using polynomial mathematical model. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1167-1178. doi: 10.3934/dcdss.2019080

[13]

Azeddine Elmajidi, Elhoussine Elmazoudi, Jamila Elalami, Noureddine Elalami. Dependent delay stability characterization for a polynomial T-S Carbon Dioxide model. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021035

[14]

Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $ \beta $-transformation. Discrete & Continuous Dynamical Systems, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267

[15]

Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1053-1065. doi: 10.3934/cpaa.2009.8.1053

[16]

Di Wu, Yanqin Bai, Fusheng Xie. Time-scaling transformation for optimal control problem with time-varying delay. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1683-1695. doi: 10.3934/dcdss.2020098

[17]

Hong Yang, Junjie Wei. Dynamics of spatially heterogeneous viral model with time delay. Communications on Pure & Applied Analysis, 2020, 19 (1) : 85-102. doi: 10.3934/cpaa.2020005

[18]

Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk. A simple model of carcinogenic mutations with time delay and diffusion. Mathematical Biosciences & Engineering, 2013, 10 (3) : 861-872. doi: 10.3934/mbe.2013.10.861

[19]

Niclas Carlsson, Göran Högnäs. Asymptotic properties of a TCP model with time-outs. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 543-564. doi: 10.3934/dcdsb.2005.5.543

[20]

Tao Pang, Azmat Hussain. An infinite time horizon portfolio optimization model with delays. Mathematical Control & Related Fields, 2016, 6 (4) : 629-651. doi: 10.3934/mcrf.2016018

 Impact Factor: 

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]