本文選題：經(jīng)驗(yàn)?zāi)B(tài)分解 + ARIMA模型　； 參考：《江西財(cái)經(jīng)大學(xué)》2017年碩士論文

【摘要】：本文應(yīng)用經(jīng)驗(yàn)?zāi)B(tài)分解和時(shí)間序列分析模型,研究義烏小商品價(jià)格指數(shù)的預(yù)測(cè)問(wèn)題。文中首先對(duì)時(shí)間序列分析、經(jīng)驗(yàn)?zāi)B(tài)分解和義烏小商品價(jià)格指數(shù)的發(fā)展歷史和研究現(xiàn)狀進(jìn)行綜合描述。隨后介紹了時(shí)間序列分析的基本理論,其中包括時(shí)間序列的平穩(wěn)性檢驗(yàn)和純隨機(jī)性過(guò)程,平穩(wěn)時(shí)間序列模型和非平穩(wěn)時(shí)間序列模型。接著詳細(xì)介紹了經(jīng)驗(yàn)?zāi)B(tài)分解(EMD)的理論知識(shí),先對(duì)瞬時(shí)頻率、本征模態(tài)函數(shù)(IMF)和特征時(shí)間尺度這三個(gè)基本概念作出解釋,然后對(duì)EMD分解的基本思想、算法流程、IMF的篩選準(zhǔn)則和分解終止的條件進(jìn)行了詳細(xì)說(shuō)明,并闡述了EMD的四個(gè)主要特點(diǎn),即自適應(yīng)性、濾波性、正交性和完備性�；谶@四個(gè)特點(diǎn),本文設(shè)計(jì)了兩種基于EMD-ARIMA模型的建模方法,且兩種方案都首先運(yùn)用EMD對(duì)原序列進(jìn)行分解。第一種方案,對(duì)分解得到的有效分量逐個(gè)建立預(yù)測(cè)模型,得出各分量預(yù)測(cè)值再相加重構(gòu),獲得最終預(yù)測(cè)結(jié)果,本文簡(jiǎn)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(duì)重構(gòu)序列建立預(yù)測(cè)模型得出最終預(yù)測(cè)結(jié)果,本文簡(jiǎn)稱為“EMD-重構(gòu)-ARIMA”建模方案。在實(shí)證研究中,首先應(yīng)用“EMD-ARIMA-重構(gòu)”建模方案對(duì)義烏小商品價(jià)格指數(shù)序列進(jìn)行預(yù)測(cè)建模,得到第一組預(yù)測(cè)結(jié)果;然后應(yīng)用“EMD-重構(gòu)-ARIMA”建模方案對(duì)相同的原序列進(jìn)行預(yù)測(cè)建模,得到第二組預(yù)測(cè)結(jié)果;最后應(yīng)用GARCH模型對(duì)相同的原序列進(jìn)行預(yù)測(cè)建模,得到第三組預(yù)測(cè)結(jié)果。隨后對(duì)三種建模方案進(jìn)行對(duì)比分析,應(yīng)用MAPE和RMSE兩項(xiàng)指標(biāo)評(píng)價(jià)模型的預(yù)測(cè)誤差。結(jié)果表明,經(jīng)EMD處理后的ARIMA模型預(yù)測(cè)誤差比傳統(tǒng)時(shí)間序列分析方法的GARCH模型預(yù)測(cè)誤差減少了近一倍,其中“EMD-ARIMA-重構(gòu)”建模方案的預(yù)測(cè)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(shí)間序列分析模型的預(yù)測(cè)精度,且對(duì)分量進(jìn)行細(xì)分化建模預(yù)測(cè)的精確度最高。本文結(jié)尾處,對(duì)完善EMD在中、長(zhǎng)期時(shí)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(xué)位授予單位】：江西財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F726

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