General expression for linear and nonlinear time series models

Abstract

The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.

Keywords

linear and nonlinear / autoregressive model / system identification / time series analysis

References

[1] Yang Shuzi, Wu Ya, Xuan Jianping. Time Series Analysis in Engineering Application. 2nd ed. Wuhan: HuazhongUniversity of Science and Technology Publishing House, 2007

[2] Zhong Binglin, Huang Ren. Introduction to Machine Fault Diagnosis. 3rd ed. Beijing: Mechanical Industry Publishing House, 2007

[3] Cao Jianfu, Han Chongzhao, Fang Yangwang. Nonlinear System Theory and Application. Xian: Xian Jiaotong University Publishing House, 2006

[4] Jean-Marc Le Caillec, Renoe Garello. Time series nonlinearity modeling: A giannakis formula type approach. Signal Processing, 2003(83): 1759 –1788

[5] Pandit S M, Wu S M. Time series and system analysis with application. John Wiley and Sons, 1983

[6] Shi Zhaoyun, Wan Dejun, Huang Ren. A structure identification method of the nonlinear time Series models. Journal of Hefei University of Technology (Natural science), 1993, 16(S1): 44–49

[7] Wu Shaomin. Study on ‘AR’ Type Nonlinear Time Series Models with Application to Engineering. Nanjing: Southeast University, 1995

[8] An Hongzhi, Chen Min. Nonlinear Time Series Analysis. Shanghai: Shanghai Science and Technology Publishing House, 1998

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg