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Renyi's information transfer between financial time series

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  • Petr Jizba
  • Hagen Kleinert
  • Mohammad Shefaat

Abstract

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.

Suggested Citation

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

    1. Batra, Luckshay & Taneja, H.C., 2020. "Evaluating volatile stock markets using information theoretic measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Aslanidis, Nektarios & Bariviera, Aurelio F. & López, Óscar G., 2022. "The link between cryptocurrencies and Google Trends attention," Finance Research Letters, Elsevier, vol. 47(PA).
    3. Ferreira, Joaquim & Morais, Flávio, 2023. "Predict or to be predicted? A transfer entropy view between adaptive green markets, structural shocks and sentiment index," Finance Research Letters, Elsevier, vol. 56(C).
    4. Xiao, Di & Wang, Jun, 2020. "Dynamic complexity and causality of crude oil and major stock markets," Energy, Elsevier, vol. 193(C).
    5. Nie, Chun-Xiao, 2023. "Time-varying characteristics of information flow networks in the Chinese market: An analysis based on sector indices," Finance Research Letters, Elsevier, vol. 54(C).
    6. Bekiros, Stelios & Jlassi, Mouna & Lucey, Brian & Naoui, Kamel & Uddin, Gazi Salah, 2017. "Herding behavior, market sentiment and volatility: Will the bubble resume?," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 107-131.
    7. Banerjee, Ameet Kumar & Akhtaruzzaman, Md & Dionisio, Andreia & Almeida, Dora & Sensoy, Ahmet, 2022. "Nonlinear nexus between cryptocurrency returns and COVID-19 news sentiment," Journal of Behavioral and Experimental Finance, Elsevier, vol. 36(C).
    8. Parthajit Kayal & Moinak Maiti, 2023. "Examining the asymmetric information flow between pairs of gold, silver, and oil: a transfer entropy approach," SN Business & Economics, Springer, vol. 3(10), pages 1-22, October.
    9. Hassad de Andrade, Liz & Moreira Antunes, Jorge Junio & Araújo de Medeiros, Antônio Mamede & Wanke, Peter & Nunes, Bernardo Pereira, 2022. "The impact of social welfare and COVID-19 stringency on the perceived utility of food apps: A hybrid MCDM approach," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    10. Theo Diamandis & Yonathan Murin & Andrea Goldsmith, 2018. "Ranking Causal Influence of Financial Markets via Directed Information Graphs," Papers 1801.06896, arXiv.org.
    11. Leonidas Sandoval Junior, 2014. "Dynamics in two networks based on stocks of the US stock market," Papers 1408.1728, arXiv.org, revised Aug 2014.
    12. 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.
    13. Caferra, Rocco, 2022. "Sentiment spillover and price dynamics: Information flow in the cryptocurrency and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    14. Ferreira, Paulo & Almeida, Dora & Dionísio, Andreia & Bouri, Elie & Quintino, Derick, 2022. "Energy markets – Who are the influencers?," Energy, Elsevier, vol. 239(PA).
    15. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2020. "Estimating a function of scale parameter of an exponential population with unknown location under general loss function," Statistical Papers, Springer, vol. 61(6), pages 2511-2527, December.

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