EMD-ARIMA模型及其在小商品价格指数预测中的应用研究

发布时间：2018-06-27 00:30

本文选题：经验模态分解 + ARIMA模型　；参考：《江西财经大学》2017年硕士论文

【摘要】：本文应用经验模态分解和时间序列分析模型,研究义乌小商品价格指数的预测问题。文中首先对时间序列分析、经验模态分解和义乌小商品价格指数的发展历史和研究现状进行综合描述。随后介绍了时间序列分析的基本理论,其中包括时间序列的平稳性检验和纯随机性过程,平稳时间序列模型和非平稳时间序列模型。接着详细介绍了经验模态分解(EMD)的理论知识,先对瞬时频率、本征模态函数(IMF)和特征时间尺度这三个基本概念作出解释,然后对EMD分解的基本思想、算法流程、IMF的筛选准则和分解终止的条件进行了详细说明,并阐述了EMD的四个主要特点,即自适应性、滤波性、正交性和完备性。基于这四个特点,本文设计了两种基于EMD-ARIMA模型的建模方法,且两种方案都首先运用EMD对原序列进行分解。第一种方案,对分解得到的有效分量逐个建立预测模型,得出各分量预测值再相加重构,获得最终预测结果,本文简称为“EMD-ARIMA-重构”建模方案。第二种方案,将分解得到的有效分量先重构,再对重构序列建立预测模型得出最终预测结果,本文简称为“EMD-重构-ARIMA”建模方案。在实证研究中,首先应用“EMD-ARIMA-重构”建模方案对义乌小商品价格指数序列进行预测建模,得到第一组预测结果;然后应用“EMD-重构-ARIMA”建模方案对相同的原序列进行预测建模,得到第二组预测结果;最后应用GARCH模型对相同的原序列进行预测建模,得到第三组预测结果。随后对三种建模方案进行对比分析,应用MAPE和RMSE两项指标评价模型的预测误差。结果表明,经EMD处理后的ARIMA模型预测误差比传统时间序列分析方法的GARCH模型预测误差减少了近一倍,其中“EMD-ARIMA-重构”建模方案的预测误差最小。最后,本文总结研究结果得出结论,EMD可大幅提高时间序列分析模型的预测精度,且对分量进行细分化建模预测的精确度最高。本文结尾处,对完善EMD在中、长期时间序列分析中的研究作出展望。
[Abstract]:In this paper, empirical mode decomposition (EMD) and time series analysis model are used to study the prediction of small commodity price index in Yiwu. In this paper, the history and research status of time series analysis, empirical mode decomposition and Yiwu commodity price index are described. Then the basic theory of time series analysis is introduced, including the stationary test of time series, pure randomness process, stationary time series model and non-stationary time series model. Then the theoretical knowledge of empirical mode decomposition (EMD) is introduced in detail. The three basic concepts of instantaneous frequency, intrinsic mode function (IMF) and characteristic time scale are explained first, and then the basic idea of EMD decomposition is given. The selection criteria of IMF and the conditions for the termination of decomposition are described in detail, and the four main characteristics of EMD, namely, adaptability, filtering, orthogonality and completeness, are described in detail. Based on these four characteristics, this paper designs two modeling methods based on EMD-ARIMA model, and both schemes use EMD to decompose the original sequence. In the first scheme, the prediction model is established one by one for the effective components obtained by decomposition, and the prediction values of each component are recombined and reconstructed, and the final prediction results are obtained. This paper is referred to as the "EMD-ARIMA- reconfiguration" modeling scheme. In the second scheme, the effective components obtained from decomposition are reconstructed first, and then the prediction model is established to obtain the final prediction results. This paper is referred to as "EMD-reconfigurable Arima" modeling scheme. In the empirical research, we first use "EMD-ARIMA- refactoring" to predict and model Yiwu commodity price index series, and then use EMD-refactor-Arima to predict the same original series. Finally, the GARCH model is used to predict the same original sequence and the third group of prediction results are obtained. Then, the three modeling schemes are compared and analyzed, and the prediction errors of the models are evaluated by MAPE and RMSE. The results show that the prediction error of Arima model treated by EMD is nearly double that of GARCH model of traditional time series analysis, and the prediction error of EMD-ARIMA- reconstruction is the least. Finally, this paper concludes that EMD can greatly improve the prediction accuracy of time series analysis model, and the precision of fine differentiation modeling and prediction of components is the highest. At the end of this paper, the research on the improvement of EMD in long-term time series analysis is prospected.
【学位授予单位】：江西财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F726

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