基于多尺度下AR(P)耦合预测模型的应用研究

Study on AR(P) Hybrid Model Based on Analysis of Multi-scale

基于多尺度分析理论,运用Mallat算法和Daubechies小波,把时间序列分解为比原始序列更单一的细节和概貌部分,并利用AR(P)模型能反映时间序列中邻近时刻间联系的特性,对序列分解后的部分进行拟合与预测,然后再由多尺度分析中的重构方法进行序列重构,由此建立耦合的预测模型。通过黄河青铜峡270多年(1724～1997)年径流时间序列的建模及验证,表明拟建的耦合模型与传统单一模型的预测精度相比,由50%提高到90%,可用于实际需要。

Respect to the characteristic of the Auto-regressive model AR(P) in different time-scale, a new hybrid model of prediction for time series is proposed based on the analysis of multi-scale. Firstly, using the method of multi-scale decomposition by the algorithm of Mallat and the wavelet of Daubechies, a time series is decomposed into two parts: detail and approximate. Secondly, two different models, which are expressed by two AR(6) models (AR1(6) and AR2(6)), are developed respectively for the two decomposed parts, and new predicted data could be got from the two models. Thirdly, by using the restructuring method of multi-scale of the Mallat and the Daubechies, the final predicted time series are obtained based on the predicted data from the two models. In the case study of annual runoff time series (1724-1997) at Qingtongxia station in Yellow River, the new hybrid model had advantages over the traditional statistic model of the AR(P) in predicted qualification-rate (the qualification-rate of the new model in the study is 90% while the traditional AR(P) is only 50%). The results show that new hybrid model has feasibility in the prediction of time series.