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Renyi's information transfer between financial time series


  • Petr Jizba
  • Hagen Kleinert
  • Mohammad Shefaat


In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentuation is controlled with Renyi's parameter q. To tackle the issue of the information flow between time series we formulate the concept of Renyi's 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 Renyian 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 from 02.04.2008 to 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 Renyi information flow between the DAX and S&P500 indices.

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  • Petr Jizba & Hagen Kleinert & Mohammad Shefaat, 2011. "Renyi's information transfer between financial time series," Papers 1106.5913,, revised Jan 2012.
  • Handle: RePEc:arx:papers:1106.5913

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    Cited by:

    1. Dimpfl, Thomas & Peter, Franziska J., 2014. "The impact of the financial crisis on transatlantic information flows: An intraday analysis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 31(C), pages 1-13.
    2. repec:eee:ecofin:v:42:y:2017:i:c:p:107-131 is not listed on IDEAS
    3. Theo Diamandis & Yonathan Murin & Andrea Goldsmith, 2018. "Ranking Causal Influence of Financial Markets via Directed Information Graphs," Papers 1801.06896,
    4. Leonidas Sandoval Junior, 2014. "Dynamics in two networks based on stocks of the US stock market," Papers 1408.1728,, revised Aug 2014.
    5. Dimpfl, Thomas & Peter, Franziska J., 2014. "The impact of the financial crisis on transatlantic information flows: An intraday analysis," University of Tuebingen Working Papers in Economics and Finance 70, University of Tuebingen, Faculty of Economics and Social Sciences.

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