【作者】 张华；

【导师】 张德生；

【作者基本信息】 西安理工大学 ， 应用数学， 2009， 硕士

【摘要】 部分线性自回归模型既含有参数分量,又含有非参数分量,兼顾了参数回归模型和非参数回归模型的优点,较单纯的参数模型或非参数模型有更大的适应性和更强的解释能力。小波分析方法是处理非平稳数据的理想工具。本文将小波分析方法和时间序列模型结合起来对我国上证指数和深证成指进行建模预测,主要内容包括：1.首先对线性自回归滑动平均(ARMA)模型中滞后阶数的选择、模型的检验和预测,以及小波函数和分解层数的确定做了一些讨论。然后,对上证指数和深证成指分别建立了ARMA模型和基于小波的ARMA模型。最后,用所建立的模型进行了拟合和预测,并分析比较了预测结果。2.讨论了部分线性自回归模型的建模理论,在估计方法上做了一些探讨,确定了滞后变量、最优模型,选择了最佳带宽,利用偏残差估计对上证指数和深证成指分别建立了部分线性自回归模型,并对建立的模型进行了有效性检验。用通过检验后的模型进行预测,与实际数据对比判断该模型的优劣。3.把小波分析和部分线性自回归模型相结合,对上证指数和深证成指分别建立了基于小波的部分线性自回归模型,并进行了拟合、预测。最后与单纯的部分线性自回归模型进行了比较,结果表明：结合小波以后预测精度有所提高。将部分线性自回归模型与线性自回归模型进行比较,结果表明：由于部分线性自回归模型综合了参数分量和非参数分量,比线性自回归模型拟合和预测的精度要高。更多还原

【Abstract】 Partially linear autoregression model with parametric variable and nonparametric variable has more adaptability and explanatory ability than the parametric model and the nonparametric model. The wavelet is a perfect tool to deal with instability signals. This thesis has established models of Shanghai stock index and Shenzhen component index based on wavelet and time series models. The contents of the thesis are as follows:1. Selection of significant variables, model test and forecast of ARMA model, selection of wavelet function and decomposition level are discussed. Then, the ARMA model and the ARMA model based on wavelet of Shanghai stock index and Shenzhen component index are established. Finally, the fitting and forecasting with two models are analyzed and compared.2. The modeling theory and the estimation method of partially linear autoregression model are discussed, and the lag variables, best model, the optimal bandwidth are determined. Partially linear autoregression models of Shanghai stock index and Shenzhen component index based on partial residual estimate are established and the validity of the model are examined. Finally, forecasting with the model and judged the effect of the model based on the real data.3. The partially linear autoregression model based on wavelet of Shanghai stock index and Shenzhen component index are established, and fitted and forecasted with these models. Then, comparing these models with the partially linear autoregression models, the result shows that time series based on wavelet has more forecasting precision. Finally, comparing these models with the linear regression models, the result shows that partially linear autoregression model with parametric variable and nonparametric variable is better than the linear autoregression model on fitting and forecasting.更多还原