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Rényi’s information transfer between financial time series

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  • Jizba, Petr
  • Kleinert, Hagen
  • Shefaat, Mohammad

Abstract

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

Suggested Citation

  • Jizba, Petr & Kleinert, Hagen & Shefaat, Mohammad, 2012. "Rényi’s information transfer between financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(10), pages 2971-2989.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:10:p:2971-2989
    DOI: 10.1016/j.physa.2011.12.064
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    Citations

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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. Neto, David, 2022. "Revisiting spillovers between investor attention and cryptocurrency markets using noisy independent component analysis and transfer entropy," The Journal of Economic Asymmetries, Elsevier, vol. 26(C).
    3. 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).
    4. 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.
    5. 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.
    6. 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).
    7. Neto, David, 2022. "Examining interconnectedness between media attention and cryptocurrency markets: A transfer entropy story," Economics Letters, Elsevier, vol. 214(C).
    8. Dima, Bogdan & Dima, Ştefana Maria & Barna, Flavia, 2014. "The signaling effect of tax rates under fiscal competition: A (Shannonian) transfer entropy approach," Economic Modelling, Elsevier, vol. 42(C), pages 373-381.
    9. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Information content of liquidity and volatility measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    10. 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).
    11. Xiao, Di & Wang, Jun, 2020. "Dynamic complexity and causality of crude oil and major stock markets," Energy, Elsevier, vol. 193(C).
    12. Neto, David, 2021. "Are Google searches making the Bitcoin market run amok? A tail event analysis," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    13. Theo Diamandis & Yonathan Murin & Andrea Goldsmith, 2018. "Ranking Causal Influence of Financial Markets via Directed Information Graphs," Papers 1801.06896, arXiv.org.
    14. Aslanidis, Nektarios & Bariviera, Aurelio F. & López, Óscar G., 2022. "The link between cryptocurrencies and Google Trends attention," Finance Research Letters, Elsevier, vol. 47(PA).
    15. Leonidas Sandoval Junior, 2014. "Dynamics in two networks based on stocks of the US stock market," Papers 1408.1728, arXiv.org, revised Aug 2014.
    16. Jizba, Petr & Korbel, Jan, 2014. "Multifractal diffusion entropy analysis: Optimal bin width of probability histograms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 438-458.
    17. Sun, Xiaotian & Fang, Wei & Gao, Xiangyun & An, Sufang & Liu, Siyao & Wu, Tao, 2021. "Time-varying causality inference of different nickel markets based on the convergent cross mapping method," Resources Policy, Elsevier, vol. 74(C).
    18. Lu, Jingen & Chen, Xiaohong & Liu, Xiaoxing, 2018. "Stock market information flow: Explanations from market status and information-related behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 837-848.
    19. 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).
    20. Ferreira, Paulo & Almeida, Dora & Dionísio, Andreia & Bouri, Elie & Quintino, Derick, 2022. "Energy markets – Who are the influencers?," Energy, Elsevier, vol. 239(PA).
    21. Xie, Wen-Jie & Yong, Yang & Wei, Na & Yue, Peng & Zhou, Wei-Xing, 2021. "Identifying states of global financial market based on information flow network motifs," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    22. D’Amico, Guglielmo & Scocchera, Stefania & Storchi, Loriano, 2018. "Financial risk distribution in European Union," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 252-267.
    23. 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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