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Multiscaling and clustering of volatility

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  • Pasquini, Michele
  • Serva, Maurizio

Abstract

The dynamics of prices in stock markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, while the distribution of returns of the most important indices is known to be a truncated Lévy, the behaviour of volatility correlations is still poorly understood. What is well known is that absolute returns have memory on a long time range, this phenomenon is known in financial literature as clustering of volatility. In this paper we show that volatility correlations are power laws with a non-unique scaling exponent. This kind of multiscale phenomenology is known to be relevant in fully developed turbulence and in disordered systems and it is pointed out here for the first time for a financial series. In our study we consider the New York Stock Exchange (NYSE) daily index, from January 1966 to June 1998, for a total of 8180 working days.

Suggested Citation

  • Pasquini, Michele & Serva, Maurizio, 1999. "Multiscaling and clustering of volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 140-147.
    • Handle: RePEc:eee:phsmap:v:269:y:1999:i:1:p:140-147
    DOI: 10.1016/S0378-4371(99)00088-6
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    Citations

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    Cited by:

    1. Chen, Cheng & Wang, Yudong, 2017. "Understanding the multifractality in portfolio excess returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 346-355.
    2. Petroni, Filippo & Serva, Maurizio, 2016. "Observability of market daily volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 838-842.
    3. Yuxin Zhao & Shuai Chang & Chang Liu, 2015. "Multifractal theory with its applications in data management," Annals of Operations Research, Springer, vol. 234(1), pages 133-150, November.
    4. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.
    5. Filippo Petroni & Maurizio Serva, 2015. "Observability of Market Daily Volatility," Papers 1503.08032, arXiv.org.
    6. Fernandez, Viviana, 2010. "Commodity futures and market efficiency: A fractional integrated approach," Resources Policy, Elsevier, vol. 35(4), pages 276-282, December.
    7. Mu, Guo-Hua & Zhou, Wei-Xing, 2008. "Relaxation dynamics of aftershocks after large volatility shocks in the SSEC index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5211-5218.
    8. Miccichè, S., 2016. "Understanding the determinants of volatility clustering in terms of stationary Markovian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 186-197.
    9. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2010. "Auto-correlated behavior of WTI crude oil volatilities: A multiscale perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5759-5768.
    10. Berardi, Luca & Serva, Maurizio, 2005. "Time and foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 403-412.
    11. Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
    12. Kim, Kyungwon & Jung, Sean S., 2014. "Empirical analysis of structural change in Credit Default Swap volatility," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 56-67.
    13. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.

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