本文關(guān)鍵詞：金融時(shí)間序列的若干問(wèn)題研究　出處：《北京交通大學(xué)》2014年碩士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 金融時(shí)間序列 股票指數(shù) 轉(zhuǎn)移熵 去趨勢(shì)交叉相關(guān)分析 隨機(jī)數(shù)據(jù)缺失

【摘要】：摘要：時(shí)間序列分析已成為金融市場(chǎng)研究的不可缺少的部分,是金融定量分析的重要方法之一。金融市場(chǎng)的許多研究成果都建立在時(shí)間序列分析的基礎(chǔ)之上,時(shí)至今日金融時(shí)間序列分析方法的重要性在世界上已被廣泛認(rèn)可。 本文研究了三種度量時(shí)間序列復(fù)雜度的方法,即內(nèi)部構(gòu)成隊(duì)列(Inner composition alignment,簡(jiǎn)稱(chēng)IOTA)方法、轉(zhuǎn)移熵(Transfer entropy)以及在去趨勢(shì)交叉相關(guān)分析(Detrended cross-correlation analysis,簡(jiǎn)稱(chēng)DCCA)基礎(chǔ)上改進(jìn)得到的多標(biāo)度DCCA方法。這三種方法分別用于探測(cè)兩個(gè)時(shí)間序列之間的耦合性、信息流和多標(biāo)度交叉相關(guān)性。 IOTA是一種用于確定短時(shí)間序列之間耦合性的方法。此方法基于使得第一個(gè)序列單調(diào)遞增的置換,然后用置換重排第二個(gè)序列,計(jì)算出交叉點(diǎn)的個(gè)數(shù),進(jìn)而求得耦合值。IOTA方法具有非對(duì)稱(chēng)的優(yōu)點(diǎn),可以確定耦合的方向性。轉(zhuǎn)移熵方法是在信息論的基礎(chǔ)上提出的,是一種基于兩個(gè)系統(tǒng)的過(guò)去記錄值及當(dāng)前觀(guān)測(cè)值來(lái)探測(cè)二者之間的信息轉(zhuǎn)移的方法。該方法具有魯棒性強(qiáng),模型無(wú)關(guān)等優(yōu)點(diǎn)。DCCA方法主要用于探測(cè)非平穩(wěn)時(shí)間序列的交叉相關(guān)性,本文在DCCA基礎(chǔ)上改進(jìn)得到的多標(biāo)度DCCA方法,獲得與標(biāo)度相關(guān)的多個(gè)交叉相關(guān)系數(shù),而不是傳統(tǒng)DCCA方法的單一系數(shù),可以探測(cè)序列在不同標(biāo)度上的交叉相關(guān)性。多標(biāo)度DCCA相較于傳統(tǒng)DCCA,提供了更豐富的交叉相關(guān)信息。 本文研究了隨機(jī)缺失數(shù)據(jù)及數(shù)據(jù)長(zhǎng)度對(duì)耦合程度、信息流的影響,發(fā)現(xiàn)了一些有趣的結(jié)論。IOTA方法適用于短時(shí)間序列的耦合性分析,當(dāng)數(shù)據(jù)長(zhǎng)度達(dá)到某一閾值即可使用,豐富了短時(shí)間序列的分析方法,同時(shí)IOTA方法有對(duì)隨機(jī)數(shù)據(jù)缺失不敏感的特點(diǎn),通過(guò)研究發(fā)現(xiàn)當(dāng)隨機(jī)數(shù)據(jù)缺失達(dá)到50%時(shí),仍然可以準(zhǔn)確計(jì)算耦合值。轉(zhuǎn)移熵方法對(duì)數(shù)據(jù)長(zhǎng)度要求較高,當(dāng)數(shù)據(jù)長(zhǎng)度達(dá)到1000時(shí)才能夠準(zhǔn)確計(jì)算轉(zhuǎn)移熵,但是凈信息流受數(shù)據(jù)長(zhǎng)度的影響較小,數(shù)據(jù)長(zhǎng)度達(dá)到200即可比較準(zhǔn)確的計(jì)算凈信息流,同時(shí),轉(zhuǎn)移熵對(duì)數(shù)據(jù)缺失比較敏感,10%的隨機(jī)缺失數(shù)據(jù)就影響了轉(zhuǎn)移熵的準(zhǔn)確性,當(dāng)隨機(jī)數(shù)據(jù)缺失比例達(dá)到90%,信息流向發(fā)生變化,此時(shí)序列之間的信息轉(zhuǎn)移被完全破壞。 另外本文還研究了金融時(shí)間序列的復(fù)雜性。由于股票市場(chǎng)與實(shí)體經(jīng)濟(jì)間存在正向關(guān)系,股票指數(shù)充當(dāng)著經(jīng)濟(jì)的晴雨表,反映經(jīng)濟(jì)的運(yùn)行狀態(tài),我們選取了六個(gè)有代表性的股票指數(shù),將這六個(gè)股票指數(shù)分為兩組,其中一組為美國(guó)股票指數(shù),包含道瓊斯指數(shù)、標(biāo)普500指數(shù)和納斯達(dá)克指數(shù),另一組為中國(guó)股票指數(shù),包含恒生指數(shù)、上證指數(shù)和深證成指。將三種方法應(yīng)用于股票指數(shù)的復(fù)雜性分析中,并且研究了金融危機(jī)對(duì)金融時(shí)間序列復(fù)雜度的影響,發(fā)現(xiàn)美國(guó)股指與中國(guó)股指之間存在明顯的復(fù)雜度差異,同一國(guó)家的股票指數(shù)的耦合性比不同國(guó)家的股票指數(shù)間的耦合性強(qiáng),股票指數(shù)之間的信息流方向是從美國(guó)股指到中國(guó)股指的,美國(guó)股指之間的交叉相關(guān)性比中國(guó)股指間的交叉相關(guān)性弱。特別的是,雖然同屬于中國(guó)股指,但是恒生指數(shù)無(wú)論是在耦合性,還是信息流及交叉相關(guān)性上,都與上證指數(shù)、深證成指有較大的差別。同時(shí)還發(fā)現(xiàn)金融危機(jī)對(duì)股票指數(shù)的耦合性、信息流及交叉相關(guān)性都有明顯影響。
[Abstract]:Abstract: time series analysis has become an indispensable part of the financial market, is one of the important methods of financial quantitative analysis. Many research results on the financial market is based on time series analysis, today the financial time series analysis method it has been widely recognized in the world.
This paper studies three kinds of methods to measure the time series complexity, i.e. internal queue (Inner composition alignment, referred to as IOTA), (Transfer entropy) and the entropy in detrended cross correlation analysis (Detrended cross-correlation analysis, referred to as DCCA) multi scaling method based on improved DCCA. The three methods respectively. For the coupling between the detection of two time series, the information flow and the multiple scale cross correlation.
IOTA is a method for determining the coupling between the short time series. This method is based on the replacement of the first sequence is monotonically increasing, and then use the replacement rearrangement of second sequences, calculate the number of intersection points, calculate the value of.IOTA coupling method has the advantages of non symmetrical, can determine the direction of the coupling transfer entropy. The method is put forward based on information theory, is one of the two systems in the past recording method of information transfer between value and current observations to detect based on two. This method has strong robustness, the advantages of.DCCA model independent method is mainly used for the detection of non cross correlation based on stationary time series. DCCA based on improved multi scale DCCA method, obtained with the standard multiple cross correlation coefficient correlation, rather than the traditional DCCA method can detect a single coefficient sequence in the intersection of the different standard Correlation. Multiscale DCCA provides more information on cross correlation than traditional DCCA.
This paper studies the random missing data and the data length of the coupling degree, influence the flow of information, found some interesting conclusions.IOTA method is suitable for analysis of coupling in short time series, when the data length reaches a threshold can be used to enrich the analysis method of short time series, while the IOTA method is not sensitive to random missing data, through the study found that when the random missing data reached 50%, still can accurately calculate the coupling value. The entropy method requires high data length, when the data length reaches 1000 can accurately calculate the transfer entropy, but net information flow by the length of the data is small, the length of the data to calculate the net information 200. A more accurate flow, at the same time, the entropy is sensitive to missing data, data missing at random 10% will affect the accuracy of transfer entropy, as a random data loss ratio of 90%, The flow of information is changing, and the transfer of information between the sequences is completely destroyed.
This paper also studied the complexity of financial time series. Because there is a positive relationship between the stock market and the real economy, stock index as a barometer of the economy, reflect the running state of the economy, we selected six representative stock index, the six stock index will be divided into two groups, one group for the United States stock index, including the Dow, S & P 500 index and the NASDAQ index, another group of Chinese stock index, including the Hang Seng Index, Shanghai stock index and Shenzhen stock index. The complexity of three methods applied to stock index analysis, and study the impact of financial crisis on the complexity of the financial time series, found that there is complex the degree of difference between the United States and Chinese stock index stock index, the coupling of the same country stock index than the coupling of different countries between the stock index, the information flow between the stock index The direction is from the United States to Chinese stock index, cross correlation between the U.S. stock index stock index China than cross correlation is weak. Especially, although belong to the China stock index, but the Hang Seng Index both in the coupling, or information flow and cross correlation, and the Shanghai Composite Index, Shenzhen Stock Index have a greater difference. It was also found that the coupling of the financial crisis on the stock index, can obviously affect the flow of information and cross correlation.

【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：O211.61;F830.91
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本文編號(hào)：1412689