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How to Measure Financial Market Efficiency? A Multifractality-Based Quantitative Approach with an Application to the European Carbon Market

Author

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  • Cristina Sattarhoff
  • Marc Gronwald
Abstract
This paper proposes a new measure for the evaluation of financial market efficiency, the so-called intermittency coefficient. This is a multifractality measure that can quantify the deviation from a random walk within the framework of the multifractal random walk model by Bacry et al. (2001b). While the random walk corresponds to the most genuine form of market efficiency, the larger the value of the intermittency coefficient is, the more inefficient a market would be. In contrast to commonly used methods based on Hurst exponents, the intermittency coefficient is a more powerful tool due to its well-established inference apparatus based on the generalised method of moments estimation technique. In an empirical application using data from the largest currently existing market for tradable pollution permits, the European Union Emissions Trading Scheme, we show that this market becomes more efficient over time. In addition, the degree of market efficiency is overall similar to that for the US stock market; for one sub-period, the market efficiency is found to be higher. While the first finding is anticipated, the second finding is noteworthy, as various observers expressed concerns with regard to the information efficiency of this newly established artificial market.

Suggested Citation

  • Cristina Sattarhoff & Marc Gronwald, 2018. "How to Measure Financial Market Efficiency? A Multifractality-Based Quantitative Approach with an Application to the European Carbon Market," CESifo Working Paper Series 7102, CESifo.
    • Handle: RePEc:ces:ceswps:_7102
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    References listed on IDEAS

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    1. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
    3. Fama, Eugene F., 1998. "Market efficiency, long-term returns, and behavioral finance," Journal of Financial Economics, Elsevier, vol. 49(3), pages 283-306, September.
    4. Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 49-83.
    5. Hintermann, Beat, 2010. "Allowance price drivers in the first phase of the EU ETS," Journal of Environmental Economics and Management, Elsevier, vol. 59(1), pages 43-56, January.
    6. Gu, Rongbao & Shao, Yanmin & Wang, Qingnan, 2013. "Is the efficiency of stock market correlated with multifractality? An evidence from the Shanghai stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 361-370.
    7. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    8. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    9. Eugenia Sanin, María & Violante, Francesco & Mansanet-Bataller, María, 2015. "Understanding volatility dynamics in the EU-ETS market," Energy Policy, Elsevier, vol. 82(C), pages 321-331.
    10. Sukpitak, Jessada & Hengpunya, Varagorn, 2016. "The influence of trading volume on market efficiency: The DCCA approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 259-265.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    12. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    13. Benz, Eva & Trück, Stefan, 2009. "Modeling the price dynamics of CO2 emission allowances," Energy Economics, Elsevier, vol. 31(1), pages 4-15, January.
    14. Ludescher, Josef & Bogachev, Mikhail I. & Kantelhardt, Jan W. & Schumann, Aicko Y. & Bunde, Armin, 2011. "On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2480-2490.
    15. Anagnostidis, P. & Varsakelis, C. & Emmanouilides, C.J., 2016. "Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 116-128.
    16. Gu, Rongbao & Chen, Hongtao & Wang, Yudong, 2010. "Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2805-2815.
    17. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    18. Lux, Thomas & Segnon, Mawuli & Gupta, Rangan, 2016. "Forecasting crude oil price volatility and value-at-risk: Evidence from historical and recent data," Energy Economics, Elsevier, vol. 56(C), pages 117-133.
    19. Wang, Yudong & Wu, Chongfeng & Yang, Li, 2016. "Forecasting crude oil market volatility: A Markov switching multifractal volatility approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 1-9.
    20. Thomas Lux, 2004. "Detecting Multifractal Properties In Asset Returns: The Failure Of The "Scaling Estimator"," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 481-491.
    21. Yudong Wang & Chongfeng Wu, 2013. "Efficiency of Crude Oil Futures Markets: New Evidence from Multifractal Detrending Moving Average Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 42(4), pages 393-414, December.
    22. Paolella, Marc S. & Taschini, Luca, 2008. "An econometric analysis of emission allowance prices," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2022-2032, October.
    23. Charles, Amélie & Darné, Olivier & Fouilloux, Jessica, 2011. "Testing the martingale difference hypothesis in CO2 emission allowances," Economic Modelling, Elsevier, vol. 28(1-2), pages 27-35, January.
    24. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
    25. Zhuang, Xiaoyang & Wei, Yu & Ma, Feng, 2015. "Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 101-113.
    26. Ning, Ye & Wang, Yiming & Su, Chi-wei, 2017. "How did China’s foreign exchange reform affect the efficiency of foreign exchange market?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 219-226.
    27. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    28. Emmanuel Bacry & Alexey Kozhemyak & J.-F. Muzy, 2008. "Continuous cascade models for asset returns," Post-Print hal-00604449, HAL.
    29. Bacry, E. & Kozhemyak, A. & Muzy, Jean-Francois, 2008. "Continuous cascade models for asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 156-199, January.
    30. repec:dau:papers:123456789/10174 is not listed on IDEAS
    31. Wang, Yudong & Liu, Li & Gu, Rongbao & Cao, Jianjun & Wang, Haiyan, 2010. "Analysis of market efficiency for the Shanghai stock market over time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1635-1642.
    32. Zhuang, Xiaoyang & Wei, Yu & Zhang, Bangzheng, 2014. "Multifractal detrended cross-correlation analysis of carbon and crude oil markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 113-125.
    33. Zhou, Weijie & Dang, Yaoguo & Gu, Rongbao, 2013. "Efficiency and multifractality analysis of CSI 300 based on multifractal detrending moving average algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1429-1438.
    34. Daskalakis, George, 2013. "On the efficiency of the European carbon market: New evidence from Phase II," Energy Policy, Elsevier, vol. 54(C), pages 369-375.
    35. Segnon, Mawuli & Lux, Thomas & Gupta, Rangan, 2017. "Modeling and forecasting the volatility of carbon dioxide emission allowance prices: A review and comparison of modern volatility models," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 692-704.
    36. Arshad, Shaista & Rizvi, Syed Aun R., 2015. "The troika of business cycle, efficiency and volatility. An East Asian perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 158-170.
    37. Beat Hintermann & Sonja Peterson & Wilfried Rickels, 2016. "Price and Market Behavior in Phase II of the EU ETS: A Review of the Literature," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 10(1), pages 108-128.
    38. J. F. Muzy & R. Baile & E. Bacry, 2013. "Random cascade model in the limit of infinite integral scale as the exponential of a non-stationary $1/f$ noise. Application to volatility fluctuations in stock markets," Papers 1301.4160, arXiv.org.
    39. Zunino, L. & Tabak, B.M. & Figliola, A. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2008. "A multifractal approach for stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6558-6566.
    40. Khediri, Karim Ben & Charfeddine, Lanouar, 2015. "Evolving efficiency of spot and futures energy markets: A rolling sample approach," Journal of Behavioral and Experimental Finance, Elsevier, vol. 6(C), pages 67-79.
    41. Rizvi, Syed Aun R. & Dewandaru, Ginanjar & Bacha, Obiyathulla I. & Masih, Mansur, 2014. "An analysis of stock market efficiency: Developed vs Islamic stock markets using MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 86-99.
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    Cited by:

    1. Zhong, Meirui & Zhang, Rui & Ren, Xiaohang, 2023. "The time-varying effects of liquidity and market efficiency of the European Union carbon market: Evidence from the TVP-SVAR-SV approach," Energy Economics, Elsevier, vol. 123(C).
    2. Fan, Xinghua & Lv, Xiangxiang & Yin, Jiuli & Tian, Lixin & Liang, Jiaochen, 2019. "Multifractality and market efficiency of carbon emission trading market: Analysis using the multifractal detrended fluctuation technique," Applied Energy, Elsevier, vol. 251(C), pages 1-1.

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    More about this item

    Keywords

    market efficiency; multifractality; multifractal random walk; European Union Emissions Trading Scheme;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • Q02 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Commodity Market
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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