應用經驗模態分解及頻譜分析重建時間序列

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Title:	應用經驗模態分解及頻譜分析重建時間序列
Other Titles:	An application of empirical mode decomposition and spectrum analysis to reconstruct time series
Authors:	白明珠;Pai, Ming-Chu
Contributors:	淡江大學管理科學研究所博士班張紘炬;Chang, Horng-Jinh
Keywords:	經驗模態分解法;累積本質模態函數;頻譜分析;價格發現;Empirical mode decomposition;Cumulative intrinsic mode functions;Spectrum analysis;price discovery
Date:	2011
Issue Date:	2011-12-28 18:16:26 (UTC+8)
Abstract:	過去對於財務經濟的數據分析，都要求該數據必須為定態資料，甚至必須為線性資料。實際上，資料往往是非定態，導致研究者經常需要進行資料的定態轉換，而此舉往往使得資料喪失原有的特徵。本研究選取2006年至2009年度，S&P500股價指數、全球鋼鐵價格指數及布蘭特原油現貨價格等，利用Huang et al.(1998)所提出的經驗模態分解程序(empirical mode decomposition, EMD)，分析非定態與非線性之時間序列資料。首先運用EMD技術，將時間序列資料，依本身的震盪特徵分解為數個分量序列與一個單調函數，分量序列即為所謂的本質模態函數(intrinsic mode functions, IMFs)。接著使用頻譜分析的技術，由頻域面界定各個IMFs之週期，再依照實務上的週期分類標準，將各IMFs合成為短期、中期與長期三個主要的分量序列，本研究稱之為累積本質模態函數(cumulative intrinsic mode functions, CIMFs)。研究結果發現三個樣本各自的CIMFs皆為定態序列，不但解決傳統時間序列分析資料必須為定態(stationary)的限制，且CIMFs皆可使用傳統的時間序列分析進行後續研究，開創了資料差分轉換的另外一條道路。本研究亦發現，若將所有的CIMFs與單調函數加總之後，可以還原為原始的時間序列資料，避免了差分轉換造成與原始資料之間的失真問題。另應用此方法，以西德州原油現貨與期貨價格時間序列資料為實證標的，再透過交叉相關係數與VAR探討其交互關係。研究結果發現，期貨短週期的變動對現貨短週期的變動具有價格發現的功能，與過去使用報酬率探討價格發現的研究結果相似。而期貨中週期的變動，同樣對於現貨中週期具有價格發現的功能，此為過去研究所沒有的發現。 Financial data of past economic analyses are either stationary or even linear. In fact, data are always non-stationary; hence, researchers often need to carry out data conversion, which may lose original features of the data. This study applies empirical mode decomposition (EMD) proposed by Huang et al. (1998) for analysis of non-stationary and nonlinear financial and economic time-series data, including S&P 500 stock index, global iron and steel price index, and Brent crude oil price from 2006 to 2009. According to fluctuation characteristics, EMD first decomposes the time series into several component series and a monotonic function. The component series are called intrinsic mode functions (IMFs). Spectral analysis utilizes the frequency domain region to define the IMF period, and aggregates the IMFs into short-, medium-, and long-term component series, which are referred to in this study as cumulative intrinsic mode functions (CIMFs). The findings show that the CIMFs of the three samples are stationary series, thus resolving the restriction on stationary data. Moreover, CIMFs use traditional time-series analysis for further studies, and provide another way for data differential conversion. The proposed approach can restore all CIMFs and one monotonic function to the raw time-series data after aggregation to avoid data distortion caused by differential conversion. This study also selects the West Texas Crude oil spot and futures prices as empirical objects. This result is consistent with previous studies on price discovery using the rate of return. Unlike previous research, this study shows that a medium-term change of futures also leads to price discovery for a medium-term change in spot prices.
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