Abstract: The classical Autoregressive Moving Average model（ARMA） and the recently promoted Functional-coefficient Autoregressive model（FAR） fail to satisfy the high request for precision and processing speed in predicting nonlinear time series. A new statistical prediction model called the Polynomial Coefficient Autoregressive model（PCAR） is put forward to improve the prediction performance. The forms of PCAR model are introduced, and then the methods of parameter-estimation and rank-decision for PCAR model are discussed in detail. The modeling algorithm based on Bayesian Information Criteria（BIC） is given. Compared to ARMA model, PCAR model can eliminate the model-selection error by enhancing the applicability, while PCAR model is characterized by parameter model, avoiding the shortcomings of the local linear regressive estimation for FAR model. The equivalence terms between PCAR model and ARMA, FAR models are researched. The conclusion is drawn by experimentation that PCAR model can achieve the best performance, with the prediction precision for one step improved respectively by 99.65% and 18.7% compared to ARMA and FAR models, and the modeling time only 0.2 percent of FAR model.

Key words: time series analysis, nonlinear prediction, autoregressive model, Autoregressive Moving Average model, Functional-coefficient Autoregressive model

摘要： 传统的自回归滑动平均模型（ARMA）和新近出现的函数系数自回归模型（FAR）不能满足非线性时间序列预测分析的准确度与运算速度要求，为了改进预测性能，研究提出了一种新的统计预测模型——多项式系数自回归模型（PCAR）。给出了PCAR模型的表示形式，详细探讨了PCAR模型的参数估计和阶次选择方法，在此基础上又提出了基于BIC准则的建模算法。同ARMA模型相比，PCAR模型扩大了适用对象范围，有效降低了模型选择误差；同FAR模型相比，它具有参数模型的特点，避免了系数函数局部线性回归估计所存在的不足；分析了PCAR模型与ARMA、FAR模型的等价条件。通过实验分析得出了PCAR模型较ARMA、FAR模型的单步预测准确度分别提高了99.65%和18.7%的结论，而且PCAR建模运算所需时间仅为FAR模型的0.2%。

关键词: 时间序列分析, 非线性预测, 自回归模型, 自回归滑动平均（ARMA）模型, 函数系数自回归（FAR）模型