多尺度熵應用於時間序列結構性變動的探討

The application of Multiscale entropy in structural changes of time series

林志強(Lin, Jr-Chia)

指導教授 ： 林財川

國立臺北大學/商學院/統計學系/碩士(2011年)

摘要

近年來，許多研究學者利用多尺度熵(multiscale entropy，簡稱MSE)，用於工程或醫學上的研究，用以分析其感興趣事物的複雜度，皆獲得獲得極佳的研究成果。因此本研究主要目的希望可以利用樣本熵(Sample entropy，簡稱SampEn)計算時間序列資料波動的複雜性，並以多尺度熵在不同時間尺度下，來探討序列資料波動的曲線變化。本研究採取大量電腦模擬資料來觀察研究，找出了可以利用多尺度熵評估時間序列資料發生結構性變化的可能時間點的方法。此方法為將原序列分成若干個子序列（需避免子序列資料筆數太少），若這些序列的多尺度熵曲線變化都相同，則此序列不具結構性變動；相對地，若曲線變化有一子序列和其他子序列不同，則此序列具結構性變動，且變動點可能存在於此子序列中。將這些多尺度熵曲線變化和其他不同的子序列再分成若干個子序列，如此反覆尋找，直到找到結構性變動點所在的小區間為止。

關鍵字

多尺度熵,結構性變動

並列摘要

In the recent years, multiscale entropy (MSE) has been widely adopted for engineering or medical researches and for analysis on the complexity of things researchers interest in, which all bringing in excellent research results. Therefore, the main purpose of this research is to use Sample entropy (SampEn) to calculate the complexity of fluctuations of time series. We use multiscale entropy at different time scales to explore the curve change of sequence data volatility. By observing and researching considerable amount of computer simulation data, we find out the way to use multiscale entropy to evaluate the possible time of structural changes of time series. Through this approach, the original sequence will be separated into several subsequences in case the data of subsequences is not enough. If the multiscale entropy curves among the sequences fluctuate in the same way, it means these sequences do not have structural changes. On the contrary, if one curve fluctuation from one subsequence is different from other subsequences’, this should mean this sequence has structural change and the change point may exist within it. These curve changes of the multiscale entropy and other different subsequences will be divided into several more subsequences; then we search over and over until we find the structural change point within the small interval.

並列關鍵字

multiscale entropy ,MSE,structural changes

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