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

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