非线性时间序列的投影寻踪建模与预报

On a Better Approach for Non-Linear Time Series Model Building and Forecasting in Engineering

非线性时间序列的投影寻踪建模与预报田铮，肖华勇非统性时间序列研究的中心问题是：对平稳过程｛Ｘｔ，ｔ∈Ｚ｝，构造一ｆ：Ｒｌ→Ｒ，使其满足其中ｆ是未知光滑函数，｛εｔ｝～ＷＮ（０，σ２），ｌ＝ｐ＋ｑ。现有的非线性时间序列分析的理论和方法本质上是针对某一非...

In signal processing, dynamic system indentification,etc, linear time series analysis becomes increasingly inadequate in precision when non-linear time series actually exists.Quite a few non-linear time series models have been proposed in recent years, but their approach is a finite parametric one with obvious limitations[2].Projection pursuit approach for non--linear time series model building and forecasting isproposed for the first time in this paper. Its model can vary with data so as to make betterforecasting possible. In this research summary, different from the Chinense text, we keepthe mathematics to a very minimum and relegate it to its last part.Using projection pursuit approach, we establish models for both Wolfer sunspot numberand the Canadian lynx number. Results for Wolfer sunsport number are shown in Fis. 1 andthe residuals are less than 5%. Results for Canadian lynx number are shown in Fig. 2 andthe residuals are less than 2. 5%. The reason why the highly satisfsctory results of less than5% and less than 2. 5% are obtained is that projection pursuit apporoach is a non-parametric one.Tong in 1990[2] pginted out the desirability of employing parametric approach but Tongand other authors have continued to employ parametric approach in their published book orpaper[1][2].Let (Xt,t∈Z} be a time series, { Xt,t∈Z } is said to follow a non-linear autoregressivemoving average model of order (p, q) if there exists a function f: Rl→R, such thatwhere f is a smoothing unkown function, {εt}￣WN (0, σ2). The projection pursuit buildingmodel for non-linear time series is to approach f(.), expressed mathematically as follows:For the Lp convergence of projection pursuit ARMA we establish Theorem 1:Theorem 1. Let f (X) be a measurable function on a l-dimensional Borel field, and,then there exist αj and gj(X) such that as m→∞where αj are real number,