金融时间序列的若干问题研究

发布时间：2018-01-12 04:26

  本文关键词：金融时间序列的若干问题研究　出处：《北京交通大学》2014年硕士论文　论文类型：学位论文

  更多相关文章： 金融时间序列 股票指数 转移熵 去趋势交叉相关分析 随机数据缺失

【摘要】：摘要：时间序列分析已成为金融市场研究的不可缺少的部分,是金融定量分析的重要方法之一。金融市场的许多研究成果都建立在时间序列分析的基础之上,时至今日金融时间序列分析方法的重要性在世界上已被广泛认可。 本文研究了三种度量时间序列复杂度的方法,即内部构成队列(Inner composition alignment,简称IOTA)方法、转移熵(Transfer entropy)以及在去趋势交叉相关分析(Detrended cross-correlation analysis,简称DCCA)基础上改进得到的多标度DCCA方法。这三种方法分别用于探测两个时间序列之间的耦合性、信息流和多标度交叉相关性。 IOTA是一种用于确定短时间序列之间耦合性的方法。此方法基于使得第一个序列单调递增的置换,然后用置换重排第二个序列,计算出交叉点的个数,进而求得耦合值。IOTA方法具有非对称的优点,可以确定耦合的方向性。转移熵方法是在信息论的基础上提出的,是一种基于两个系统的过去记录值及当前观测值来探测二者之间的信息转移的方法。该方法具有鲁棒性强,模型无关等优点。DCCA方法主要用于探测非平稳时间序列的交叉相关性,本文在DCCA基础上改进得到的多标度DCCA方法,获得与标度相关的多个交叉相关系数,而不是传统DCCA方法的单一系数,可以探测序列在不同标度上的交叉相关性。多标度DCCA相较于传统DCCA,提供了更丰富的交叉相关信息。 本文研究了随机缺失数据及数据长度对耦合程度、信息流的影响,发现了一些有趣的结论。IOTA方法适用于短时间序列的耦合性分析,当数据长度达到某一阈值即可使用,丰富了短时间序列的分析方法,同时IOTA方法有对随机数据缺失不敏感的特点,通过研究发现当随机数据缺失达到50%时,仍然可以准确计算耦合值。转移熵方法对数据长度要求较高,当数据长度达到1000时才能够准确计算转移熵,但是净信息流受数据长度的影响较小,数据长度达到200即可比较准确的计算净信息流,同时,转移熵对数据缺失比较敏感,10%的随机缺失数据就影响了转移熵的准确性,当随机数据缺失比例达到90%,信息流向发生变化,此时序列之间的信息转移被完全破坏。 另外本文还研究了金融时间序列的复杂性。由于股票市场与实体经济间存在正向关系,股票指数充当着经济的晴雨表,反映经济的运行状态,我们选取了六个有代表性的股票指数,将这六个股票指数分为两组,其中一组为美国股票指数,包含道琼斯指数、标普500指数和纳斯达克指数,另一组为中国股票指数,包含恒生指数、上证指数和深证成指。将三种方法应用于股票指数的复杂性分析中,并且研究了金融危机对金融时间序列复杂度的影响,发现美国股指与中国股指之间存在明显的复杂度差异,同一国家的股票指数的耦合性比不同国家的股票指数间的耦合性强,股票指数之间的信息流方向是从美国股指到中国股指的,美国股指之间的交叉相关性比中国股指间的交叉相关性弱。特别的是,虽然同属于中国股指,但是恒生指数无论是在耦合性,还是信息流及交叉相关性上,都与上证指数、深证成指有较大的差别。同时还发现金融危机对股票指数的耦合性、信息流及交叉相关性都有明显影响。
[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.

【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O211.61;F830.91
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本文编号：1412689