本文選題：經(jīng)驗模態(tài)分解 + ARIMA模型　； 參考：《江西財經(jīng)大學》2017年碩士論文

【摘要】：本文應用經(jīng)驗模態(tài)分解和時間序列分析模型,研究義烏小商品價格指數(shù)的預測問題。文中首先對時間序列分析、經(jīng)驗模態(tài)分解和義烏小商品價格指數(shù)的發(fā)展歷史和研究現(xiàn)狀進行綜合描述。隨后介紹了時間序列分析的基本理論,其中包括時間序列的平穩(wěn)性檢驗和純隨機性過程,平穩(wěn)時間序列模型和非平穩(wěn)時間序列模型。接著詳細介紹了經(jīng)驗模態(tài)分解(EMD)的理論知識,先對瞬時頻率、本征模態(tài)函數(shù)(IMF)和特征時間尺度這三個基本概念作出解釋,然后對EMD分解的基本思想、算法流程、IMF的篩選準則和分解終止的條件進行了詳細說明,并闡述了EMD的四個主要特點,即自適應性、濾波性、正交性和完備性�；谶@四個特點,本文設(shè)計了兩種基于EMD-ARIMA模型的建模方法,且兩種方案都首先運用EMD對原序列進行分解。第一種方案,對分解得到的有效分量逐個建立預測模型,得出各分量預測值再相加重構(gòu),獲得最終預測結(jié)果,本文簡稱為“EMD-ARIMA-重構(gòu)”建模方案。第二種方案,將分解得到的有效分量先重構(gòu),再對重構(gòu)序列建立預測模型得出最終預測結(jié)果,本文簡稱為“EMD-重構(gòu)-ARIMA”建模方案。在實證研究中,首先應用“EMD-ARIMA-重構(gòu)”建模方案對義烏小商品價格指數(shù)序列進行預測建模,得到第一組預測結(jié)果;然后應用“EMD-重構(gòu)-ARIMA”建模方案對相同的原序列進行預測建模,得到第二組預測結(jié)果;最后應用GARCH模型對相同的原序列進行預測建模,得到第三組預測結(jié)果。隨后對三種建模方案進行對比分析,應用MAPE和RMSE兩項指標評價模型的預測誤差。結(jié)果表明,經(jīng)EMD處理后的ARIMA模型預測誤差比傳統(tǒng)時間序列分析方法的GARCH模型預測誤差減少了近一倍,其中“EMD-ARIMA-重構(gòu)”建模方案的預測誤差最小。最后,本文總結(jié)研究結(jié)果得出結(jié)論,EMD可大幅提高時間序列分析模型的預測精度,且對分量進行細分化建模預測的精確度最高。本文結(jié)尾處,對完善EMD在中、長期時間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.
【學位授予單位】：江西財經(jīng)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224;F726

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本文編號：2071992