具有趋势项的残差自回归移动平均模型的修正预测

A Correcting Prediction Method of Residual ARMA Models with Polynomial Trend

摘要: 为了研究新数据产生背景下时序模型的预测问题，本文针对含多项式趋势项的残差ARMA模型探讨了无需重新拟合的不变模型修正预测法。采用K折交叉验证，并以平均RMSE作为评价指标，确定最佳的多项式拟合次数。基于最小二乘法和线性时间序列建模方法进行了数值模拟和实证分析。结果显示，与需要重新拟合的改变模型修正预测法相比，无需重新拟合的不变模型修正预测法具有一定的优越性，计算成本小，且优于传统的未修正预测法，可以看作是一种简单易行的修正预测方法。

Abstract: In order to investigate the predictive issues of time series models under the context of new data generation, an invariant model correcting prediction method of residual ARMA models with polynomial trend components is discussed in this paper. K-fold cross-validation is used to determine the optimal degree of polynomial fitting in the sense of the average root mean squared error (RMSE). Numerical simulation and empirical analysis are conducted based on the least squares method and linear time series modeling approach. The results show that the invariant model correcting prediction method, which does not need to re-estimate models and has lower computational cost, exhibits certain advantages over the changing model correcting prediction method. Furthermore, the invariant model correcting prediction method outperforms the traditional uncorrected prediction method. Thus, the invariant model correcting prediction method can be viewed as a simple and feasible correcting prediction approach.