R茅nyi鈥檚 information transfer between financial time series

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• 作者：Petr Jizba^a ; ^b ; ^{jizba@physik.fu-berlin.de} ; ^{p.jizba@fjfi.cvut.cz} ; Hagen Kleinert^a ; ^c ; ^{kleinert@physik.fu-berlin.de} ; Mohammad Shefaat^d ; ^{mohammad.shefaat@quirinbank.de}
• 关键词：Econophysics ; Ré ; nyi entropy ; Information transfer ; Financial time series
• 刊名：Physica A
• 出版年：2012
• 期刊代码：138_03784371
• 类别：et
• 出版时间：15 May, 2012
• 卷：391
• 期：10
• 页码：2971-2989
• 文件大小：1461 K

摘要

In this paper, we quantify the statistical coherence between financial time series by means of the R茅nyi entropy. With the help of Campbell鈥檚 coding theorem, we show that the R茅nyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentuation is controlled with R茅nyi鈥檚 parameter . To tackle the issue of the information flow between time series, we formulate the concept of R茅nyi鈥檚 transfer entropy as a measure of information that is transferred only between certain parts of underlying distributions. This is particularly pertinent in financial time series, where the knowledge of marginal events such as spikes or sudden jumps is of a crucial importance. We apply the R茅nyian information flow to stock market time series from 11 world stock indices as sampled at a daily rate in the time period 02.01.1990-31.12.2009. Corresponding heat maps and net information flows are represented graphically. A detailed discussion of the transfer entropy between the DAX and S&P500 indices based on minute tick data gathered in the period 02.04.2008-11.09.2009 is also provided. Our analysis shows that the bivariate information flow between world markets is strongly asymmetric with a distinct information surplus flowing from the Asia-Pacific region to both European and US markets. An important yet less dramatic excess of information also flows from Europe to the US. This is particularly clearly seen from a careful analysis of R茅nyi information flow between the DAX and S&P500 indices.