Information flow between stock indices

Using transfer entropy, we observed the strength and direction of information flow between stock indices. We uncovered that the biggest source of information flow is America. In contrast, the Asia/Pacific region the biggest is receives the most information. According to the minimum spanning tree, the GSPC is located at the focal point of the information source for world stock markets. Introduction. – Economic systems have recently become an active field of research for physicists striving to transfer concepts and methodologies from statistical physics such as phase transition, fractal theory, spin models, complex networks, and information theory to the analysis of economic problems [1–24]. Among the numerous methodologies put forward, time series analysis has proven to be one of the most efficient methods and is widely applied to the examination of characteristics of stock and foreign exchange markets. In order to analyze financial time series, a range of statistical measures have been introduced, including probability distribution [20–26], autocorrelation [23], multi-fractal [27], complexity [18–20], entropy density [19, 20], and transfer entropy [11]. Information is a keyword in analyzing financial market data or in estimating the stock price of a given company. It is quantified through a variety of methods such as crosscorrelation, autocorrelation, and complexity. However, while they may be appropriate measures for the observation of the internal structure of information flow, they fail to illuminate the directionality of information flow. Schreiber [28] introduced transfer entropy, which measures the dependency in time between two variables and notes the directionality of information flow. This concept of transfer entropy has already been applied to the analysis of financial time series. Marschinski and Kantz [29] calculated information flow between the Dow Jones and DAX stock indexes to better observe interactions between the two huge markets. Kwon and Yang [11] measured the di(a)Corresponding author. rection of information flow between the composite stock index and individual stock prices, while the information flow among individual stocks in a stock market has been estimated by Baek and coauthors [30] in order to measure the internal structure of a stock market. Through transfer entropy, this paper focuses quantitatively on the direction of information flow between 25 stock markets to determine which market serves as a source of information for global stock indices. Drawn from the economic system, a plethora of empirical data reflecting economic conditions can be obtained. The time series of a composite stock price index provides prime data accurately reflecting economic conditions. Therefore, we analyzed the daily time series of the 25 stock indices listed in Table 1 for the period of 2000 – 2007 using transfer entropy in order to examine the information flow between stock markets and identify the hub. Transfer entropy. – Transfer entropy, which measures the directionality of a variable with respect to time was recently introduced by Schreiber [28] based on the probability density function (PDF). Let us consider two discrete and stationary process, I and J . Transfer entropy relates k previous samples of process I and l previous samples of process J and is defined as follows: TJ→I = ∑ p(it+1, i (k) t , j (l) t ) log p(it+1 | i (k) t , j (l) t ) p(it+1 | i (k) t ) , (1) where it and jt represent the discrete states at time t of I and J , respectively. i (k) t and j (l) t denote k and l dimensional delay vectors of two time consequences I and J ,