递进自回归预测方法

提出递进自回归预测方法，其中包括递进自回归模型、递进自回归滑动平均模型、递进时变自回归模型、递进时变自回归滑动平均模型、递进回归一自回归模型。建立时间序列的递进预测公式，给出其最佳无偏预测，并推导出递进均方误差计算公式和高置信水平的递进预测区间估计。该方法是以逐步线性形式表示的一种非线性预测，既具有线性预测的简单性，又具有非线性预测精度高的特点。它不但可用于平稳时间序列预测，而且还可用于非平稳时间序列预测、确定性时间序列预测和小样本预测。此外，文中还给出时问序列线性组合及乘积的预测方法。并通过加权累加、倒数变换等方法，对观测值进行映射变换，使其呈现出更强的规律性，以进一步提高预测精度。

PROGRESSIVE AUTOREGRESSIVE PREDICTION METHOD

A progressive autoregressive prediction method is presented, which includes the progressive autoregression (PAR), the progressive autoregressive moving average (PARMA), the progressive time-varying autoregression (PTVAR), the progressive time-varying autoregressive moving average (PTVARMA), the progressive regression and autoregression (PRAR) model. Their prediction formulas, mean square errors and confidence interval estimates are established. In this method, the autoregressive, the moving average and the regressive coefficients are corrected according to previous predicting results, and the next prediction can have higher precision than traditional method. As the method is nonlinear prediction, the PAR and the PARMA model are different from the autoregression (AR) and the autoregressive moving average (ARMA) model, which can be used to predict the covariance stationary, the nonstationary, and the deterministic series. Furthermore, the regularity of test data can be greatly enhanced by weighted accumulative addition, reciprocal transformation and so on, which raises the precision of the prediction in time series.