短记忆性时间序列的建模分析及预测

Research on the Time Series of Short Memory and Forecast

AR模型作为时间序列模型的一种,由于其参数估计和定阶简单而广泛用于系统辨识。在多维AR序列的最小二乘建模的基础上,结合Kalman滤波算法,推导了应用Kalman滤波技术的多维AR序列参数估计方法。该算法无需保存历史数据,可对AR模型的估计参数进行实时的修正。在确定AR模型阶数时,提出了两步F检验法。选取上证某A股收益序列作为样本,利用时间序列相关性分析对该算法的有效性进行验证;对时间序列的RMSE和MAD指标进行比较,结果表明该算法大大减少了建模过程中的计算工作量,并具有较好的预测性。

AR series, as one of time series models, is applied broadly in system identification because its parameter estimation and rank decision are simple. On the basis of multi - dimension AR series modeled by least sequence criterion and the Kalman filtering technique, a method for estimating parameters of multi - dimensional AR series by Kalman filtering is developed in this paper. Because it is not necessary to keep historical data for this method, the estimated parameters of AR series can be updated real - time. The two step F - tested method is proposed in the decision of rank of AR series. The series of some A stock of Shanghai stock market are chosen as swatch. By analyzing the relativity of time series, this method is validated. By comparing the index of RMSE and MAD, the result shows that this method can decrease much modeling calculation work and has good forecasting capability.