基于分数阶差分的ARFIMA模型及预测效果研究

采用MRS分析法对香港恒生指数周数据序列的长期记忆性进行研究,并建立ARFIMA模型,推导了分数阶差分的计算过程。对分数阶差分的ARFIMA模型与一阶差分的ARFIMA模型进行了比较,发现应进行分数阶差分的序列,简化成一阶差分后,就有可能丢失许多有价值的信息,导致建模误差增大。进一步使用ARFIMA模型预测公式进行预测,结果显示ARFIMA模型预测效果不理想。在对香港恒生指数周数据进行预测时,ARFIMA模型几乎是失效的,并从两个不同的角度论证了这一结果出现的必然性。

Study of ARFIMA Model and Its Forecast Performance Based on Fractional Differencing

The long-term memory of HongKong Hang Sheng index using MRS analysis was studied,established ARFIMA model for it,and detailed the procedure of fractional differencing.Furthermore,we compared the ARFIMA model built by this means with the one that took first order differencing as an alternative.The result showed that,if doing so,many useful information of time series would be lost.The forecast formula of ARFIMA model was corrected according to the method of fractional differencing,and was employed in the empirical study.It was illustrated that the forecast performance of ARFIMA model was not as not as we expected since the ARFIMA model was ineffective in forecasting Hang Sheng index.The certainty of this conclusion was proposed from two different aspects.