【作者】 李鹏飞；

【导师】 徐厚宝；

【作者基本信息】 北京理工大学 ， 应用统计（专业学位）， 2016， 硕士

【摘要】 如今股票市场预测已经成为现代金融研究的核心问题之一,本文在前人研究的基础上,意在探索出一种针对股票市场的组合预测模型,以期减少预测误差,提高预测准确度。本文所用的数据为2010年1月4日至2016年3月11日的标准普尔500指数的日收盘价,以四年的标准普尔500指数日收盘价为样本数据建立模型,并预测样本数据外6天的股指收盘价,共做了50组实验。文中首先利用自回归移动平均(ARMA)模型对实验数据进行建模和预测,虽然该模型可以很好地拟合线性关系,但是由于其非线性映射能力弱,且难以确定最优的模型结构,因此预测效果不佳。然后利用广义回归神经网络(GRNN)模型对实验数据进行建模和预测,该模型具有较强的非线性映射能力,计算速度快,且只有一个人为确定的参数,但是其预测效果与ARMA模型相差不大。最后通过探索ARMA与GRNN的恰当组合,得到预测效果相对较优的ARMA(1,1)-GRNN并利用其进行短期预测,其中ARMA(1,1)部分反映了时间序列当前观测值与前一期观测值和前一期随机干扰的关系,即将GRNN模型中融入了股价前期数据的统计特征。通过对比三个模型的预测结果得出以下结论:1).在趋势预测方面,有90%的实验组ARMA(1,1)-GRNN模型的预测效果既优于ARMA模型又优于GRNN模型,且趋势预测准确率较高,有94%的实验组ARMA(1,1)-GRNN模型的趋势预测正确率在83.33%及其以上。2).在预测误差方面,从误差平方和角度来看,有98%的实验组ARMA(1,1)-GRNN模型的预测效果优于ARMA模型和GRNN模型;从相对误差角度来看,有98%的实验组ARMA(1,1)-GRNN模型的预测效果优于ARMA模型和GRNN模型,且其预测精度较高,有94%的实验组ARMA(1,1)-GRNN模型预测值的相对误差均在1%以内;从绝对误差的角度来看,98%的实验组中ARMA(1,1)-GRNN模型的预测效果优于ARMA模型和GRNN模型。因此可以看出在标准普尔500指数短期预测中ARMA(1,1)-GRNN模型的预测效果优于ARMA模型和GRNN模型,说明单一模型通过恰当的组合可以得到预测效果较优的组合模型。更多还原

【Abstract】 The stock market prediction has become one of the core issues of modern financial research.In this paper,in order to reduce the prediction error and improve the accuracy of model forecast,I want to explore a kind of combination forecast model of the stock market on the basis of predecessors’ research.In this paper,the data is the daily closing price of S&P 500 Index from January 4th,2010 to March 11 th,2016.We use four years data as the sample data to build models,and forecast the closing price of following six days,which is used to test the forecasting effect of the models based on 50 experiments.In this paper,first of all,we use the method of autoregressive moving average to bulid model and make forecast.The model can fit linear relationship well,but it is weak in nonlinear mapping,and it is difficult to determine the optimal model structure.Thus the forecasting effect is not good.Then we build the generalized regression neural network model which is used to make forecast.The neural network model has strong ability in nonlinear mapping.Its computing speed is fast,and it has only one subjective parameter.But the forecasting effect between ARMA and GRNN has little difference.Finally,by exploring the appropriate combination of ARMA model and GRNN model,we can obtain ARMA(1,1)-GRNN model,which has better forecasting effect when we use it to make short-term forecast.ARMA(1,1)reflects the relationships between the current time series observations and previous observations and its previous random disturbance,that is to say ARMA(1,1)shares the preliminary data statistical characteristic into the GRNN model.We can draw conclusions by comparing the forecast results of the three models: 1).In terms of trend forecast,there are 90% experimental groups,in which forecasting effect of ARMA(1,1)-GRNN model is better than ARMA model and GRNN model,and the trend forecast accuracy of ARMA(1,1)-GRNN model is high.There are 94% experimental groups,in which the trend forecast accuracy of ARMA(1,1)-GRNN model is at 83.33% and above.2).In the aspect of prediction error,from the point of error sum of squares,there are 98% experimental groups,in which forecasting effect of ARMA(1,1)-GRNN model is better than ARMA model and GRNN model;From the point of the relative error,there are 98% experimental groups,in which the forecasting effect of ARMA(1,1)-GRNN model is better than ARMA model and GRNN model,and the forecast precision of ARMA(1,1)-GRNN model is high,ARMA(1,1)-GRNN model forecast relative error is within 1% in the 94% experimental groups;From the point of absolute error,there are 98% experimental groups,in which forecasting effect of ARMA(1,1)-GRNN model is better than ARMA model and GRNN model.So it can be seen that the forecasting effect of ARMA(1,1)-GRNN model is better than ARMA model and GRNN model in the short-term forecast by using S&P 500 Index.The results show that we can improve the forecasting effect by combining single models appropriately.更多还原