Some Studies On Financial Time Series

ABSTRACT:Time series analysis has become an indispensable part of the financial market research and it is one of the important financial quantitative analysis methods. Many research achievements of financial markets are raised based on the basis of time series analysis. Today the importance of time series analysis method has been widely recognized in the world.In this paper, we study three time series complexity methods, namely Inner composition alignment (IOTA) method, transfer entropy, multi-scale DCCA. These three methods are used to investigate the degree of coupling, the net transfer of information and the direction of information flow and multi-scale cross-correlation between the two series, respectively.IOTA is a method to measure the degree of coupling between the short series. This method is based on a sequence that let the series monotonically increase. IOTA method has the advantages of asymmetry, thus the direction of coupling can be determined. Transfer entropy method is proposed on the basis of information theory, and it is based on the past record and current values of the two observation methods to detect the transfer information between the two series. The method is of robust and strong, independent model. Detrended cross-correlation analysis (DCCA) method is primarily used to detect cross-correlation between non-stationary time series. Multi-scale DCCA is proposed by the improvement in this article, and can be used to obtain multiple cross-correlation coefficients as a function of scale, rather than the single coefficient of DCCA method. Compared with DCCA, multi-scale DCCA could provide richer cross-correlation information.We study the effect of random missing data and data length on the degree of coupling, the net transfer of information and the flow of information, and we find some interesting conclusions, although IOTA method applies to short sequence, it is not sensitive to the random missing data, although the percent of missing data reach to50%, the coupling value can still be calculated accurately. On the contrary, the transfer entropy applies to long series, when the length of data reach to200, it is quite accurate to calculate the net information flow. What’s more, it is more sensitive to missing data,10%missing data have an impact of the accuracy of the transfer entropy, while when the random missing data ratio reach to90%, the direction of information transfer is also changed. There is a positive relationship between the stock market and the real economy, the stock index acts as a barometer of the economy, reflecting the operating state of the economy. We selected six representative stock indices, three U.S. stock indices, which are the Dow Jones Indexes, S&P500and Nasdaq Composite Index, three of China’s stock indices, which are the Hang Seng Index, the Shanghai Composite Index and Compositional Index of Shenzhen Stock Market. The three methods used in complex analysis between two groups stock indices and the group interior, and the effects of the financial crisis on the complexity of financial time series. We find that the U.S. stock indices and China stock indices show quite different degree of coupling and cross-correlation, the coupling strength between U.S. stock indices are stronger than that between U.S. indices and China indices, the cross-correlation between U.S. indices are weaker than that between U.S. indices and China indices. The direction of information flow between stock indices are from the U.S. indices to China indices, in particular, In particular, Hang Seng Index have great difference in coupling, transfer information and cross-correlation with Shanghai Composite Index and Compositional Index of Shenzhen Stock Market. We also found that the financial crisis has a significant effect on the coupling, information flow and cross-correlation of the stock indices.