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Information measure for financial time series: quantifying short-term market heterogeneity

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  • Linda Ponta
  • Anna Carbone

Abstract

A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked according to their size to form a probability distribution function and finally fed in the expression of the Shannon entropy. In this work, such entropy measure is implemented on the time series of prices and volatilities of six financial markets. The analysis has been performed, on tick-by-tick data sampled every minute for six years of data from 1999 to 2004, for a broad range of moving average windows and volatility horizons. The study shows that the entropy of the volatility series depends on the individual market, while the entropy of the price series is practically a market-invariant for the six markets. Finally, a cumulative information measure - the `Market Heterogeneity Index'- is derived from the integral of the proposed entropy measure. The values of the Market Heterogeneity Index are discussed as possible tools for optimal portfolio construction and compared with those obtained by using the Sharpe ratio a traditional risk diversity measure.

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  • Linda Ponta & Anna Carbone, 2017. "Information measure for financial time series: quantifying short-term market heterogeneity," Papers 1710.07331, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1710.07331
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    Cited by:

    1. Ponta, Linda & Murialdo, Pietro & Carbone, Anna, 2021. "Information measure for long-range correlated time series: Quantifying horizon dependence in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    2. Masoud Ahmadipour & Hashim Hizam & Mohammad Lutfi Othman & Mohd Amran Mohd Radzi, 2018. "An Anti-Islanding Protection Technique Using a Wavelet Packet Transform and a Probabilistic Neural Network," Energies, MDPI, vol. 11(10), pages 1-31, October.
    3. Charu Sharma & Amber Habib, 2019. "Mutual information based stock networks and portfolio selection for intraday traders using high frequency data: An Indian market case study," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-19, August.
    4. Shouzhen Zeng & Shahzaib Asharf & Muhammad Arif & Saleem Abdullah, 2019. "Application of Exponential Jensen Picture Fuzzy Divergence Measure in Multi-Criteria Group Decision Making," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    5. Pietro Murialdo & Linda Ponta & Anna Carbone, 2020. "Long-Range Dependence in Financial Markets: a Moving Average Cluster Entropy Approach," Papers 2004.14736, arXiv.org.
    6. Qin, Guyue & Shang, Pengjian, 2021. "Analysis of time series using a new entropy plane based on past entropy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Assaf, Ata & Charif, Husni & Demir, Ender, 2022. "Information sharing among cryptocurrencies: Evidence from mutual information and approximate entropy during COVID-19," Finance Research Letters, Elsevier, vol. 47(PA).
    8. Wei Dong & Qiang Yang & Xinli Fang, 2018. "Multi-Step Ahead Wind Power Generation Prediction Based on Hybrid Machine Learning Techniques," Energies, MDPI, vol. 11(8), pages 1-19, July.
    9. V Dimitrova & M Fernández-Martínez & M A Sánchez-Granero & J E Trinidad Segovia, 2019. "Some comments on Bitcoin market (in)efficiency," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-14, July.

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