IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1609.04199.html

Entropy and efficiency of the ETF market

Author

Listed:
  • Lucio Maria Calcagnile
  • Fulvio Corsi
  • Stefano Marmi

Abstract

We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-minute and 5-minute price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate true inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure.

Suggested Citation

  • Lucio Maria Calcagnile & Fulvio Corsi & Stefano Marmi, 2016. "Entropy and efficiency of the ETF market," Papers 1609.04199, arXiv.org.
    • Handle: RePEc:arx:papers:1609.04199
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/1609.04199
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Oh, Gabjin & Kim, Seunghwan & Eom, Cheoljun, 2007. "Market efficiency in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 209-212.
    2. Armin Shmilovici & Yoav Kahiri & Irad Ben-Gal & Shmuel Hauser, 2009. "Measuring the Efficiency of the Intraday Forex Market with a Universal Data Compression Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 33(2), pages 131-154, March.
    3. Armin Shmilovici & Yael Alon-Brimer & Shmuel Hauser, 2003. "Using a Stochastic Complexity Measure to Check the Efficient Market Hypothesis," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 273-284, October.
    4. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
    5. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    6. Giglio, Ricardo & Matsushita, Raul & Figueiredo, Annibal & Gleria, Iram & Da Silva, Sergio, 2008. "Algorithmic complexity theory and the relative efficiency of financial markets - Updated," MPRA Paper 11150, University Library of Munich, Germany.
    7. Giglio, Ricardo & Matsushita, Raul & Figueiredo, Annibal & Gleria, Iram & Da Silva, Sergio, 2008. "Algorithmic complexity theory and the relative efficiency of financial markets," MPRA Paper 8704, University Library of Munich, Germany.
    8. Wiston Adrian Risso, 2009. "The informational efficiency: the emerging markets versus the developed markets," Applied Economics Letters, Taylor & Francis Journals, vol. 16(5), pages 485-487.
    9. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    10. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. is not listed on IDEAS
    2. Silvia Onofri & Andrey Shternshis & Stefano Marmi, 2025. "Emergence of Randomness in Temporally Aggregated Financial Tick Sequences," Papers 2511.17479, arXiv.org.
    3. Andrey Shternshis & Piero Mazzarisi & Stefano Marmi, 2022. "Efficiency of the Moscow Stock Exchange before 2022," Papers 2207.10476, arXiv.org, revised Jul 2022.
    4. Shternshis, Andrey & Mazzarisi, Piero & Marmi, Stefano, 2022. "Measuring market efficiency: The Shannon entropy of high-frequency financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Andrey Shternshis & Stefano Marmi, 2023. "Price predictability at ultra-high frequency: Entropy-based randomness test," Papers 2312.16637, arXiv.org, revised May 2024.
    6. Andrey Shternshis & Piero Mazzarisi, 2022. "Variance of entropy for testing time-varying regimes with an application to meme stocks," Papers 2211.05415, arXiv.org, revised Jun 2023.
    7. Andrey Shternshis & Piero Mazzarisi, 2024. "Variance of entropy for testing time-varying regimes with an application to meme stocks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 215-258, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shternshis, Andrey & Mazzarisi, Piero & Marmi, Stefano, 2022. "Measuring market efficiency: The Shannon entropy of high-frequency financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Jean-Yves Gnabo & J�rôme Lahaye & S�bastien Laurent & Christelle Lecourt, 2012. "Do jumps mislead the FX market?," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1521-1532, October.
    3. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    4. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Econometric modeling of exchange rate volatility and jumps," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 16, pages 373-427, Edward Elgar Publishing.
    5. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    6. Matsushita, Raul & Brandão, Helena & Nobre, Iuri & Da Silva, Sergio, 2024. "Differential entropy estimation with a Paretian kernel: Tail heaviness and smoothing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 646(C).
    7. Giacomo Bormetti & Lucio Maria Calcagnile & Michele Treccani & Fulvio Corsi & Stefano Marmi & Fabrizio Lillo, 2015. "Modelling systemic price cojumps with Hawkes factor models," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1137-1156, July.
    8. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    9. Gael M. Martin & Andrew Reidy & Jill Wright, 2009. "Does the option market produce superior forecasts of noise-corrected volatility measures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 77-104.
    10. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2016. "Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach," CREATES Research Papers 2016-27, Department of Economics and Business Economics, Aarhus University.
    11. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    12. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2010. "Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1891-1901.
    13. Brandouy, Olivier & Delahaye, Jean-Paul & Ma, Lin & Zenil, Hector, 2014. "Algorithmic complexity of financial motions," Research in International Business and Finance, Elsevier, vol. 30(C), pages 336-347.
    14. Cheng, Mingmian & Swanson, Norman R. & Yang, Xiye, 2021. "Forecasting volatility using double shrinkage methods," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 46-61.
    15. Abounoori, Esmaiel & Shahrazi, Mahdi & Rasekhi, Saeed, 2012. "An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3170-3179.
    16. Massimiliano Caporin & Angelo Ranaldo & Gabriel G. Velo, 2015. "Precious metals under the microscope: a high-frequency analysis," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 743-759, May.
    17. Dimitriadis, Timo & Halbleib, Roxana & Polivka, Jeannine & Rennspies, Jasper & Streicher, Sina & Wolter, Axel Friedrich, 2026. "Efficient sampling for realized variance estimation in time-changed diffusion models," Journal of Econometrics, Elsevier, vol. 254(PA).
    18. Corradi, Valentina & Distaso, Walter & Swanson, Norman R., 2009. "Predictive density estimators for daily volatility based on the use of realized measures," Journal of Econometrics, Elsevier, vol. 150(2), pages 119-138, June.
    19. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    20. Ortiz-Cruz, Alejandro & Rodriguez, Eduardo & Ibarra-Valdez, Carlos & Alvarez-Ramirez, Jose, 2012. "Efficiency of crude oil markets: Evidences from informational entropy analysis," Energy Policy, Elsevier, vol. 41(C), pages 365-373.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1609.04199. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.