1,362
Views
2
CrossRef citations to date
0
Altmetric
Research Article

On the statistics of scaling exponents and the multiscaling value at risk

&
Pages 1361-1382 | Received 03 Feb 2020, Accepted 15 Mar 2021, Published online: 02 Apr 2021

References

  • Antoniades, I. P., Giuseppe Brandi, L. Magafas, and T. Di Matteo. 2021. “The Use of Scaling Properties to Detect Relevant Changes in Financial Time Series: A New Visual Warning Tool.” Physica A: Statistical Mechanics and Its Applications 565: 125561.
  • Bacry, Emmanuel, Jean Delour, and Jean-François Muzy. 2001a. “Modelling Financial Time Series Using Multifractal Random Walks.” Physica A: Statistical Mechanics and Its Applications 299 (1): 84–92.
  • Bacry, Emmanuel, Jean Delour, and Jean-François Muzy. 2001b. “Multifractal Random Walk.” Physical Review E 64 (2): 026103.
  • Bacry, Emmanuel, Alexey Kozhemyak, and Jean-François Muzy. 2008. “Continuous Cascade Models for Asset Returns.” Journal of Economic Dynamics and Control 32 (1): 156–199.
  • Bacry, Emmanuel, Alexey Kozhemyak, and Jean-François Muzy. 2013. “Log-Normal Continuous Cascade Model of Asset Returns: Aggregation Properties and Estimation.” Quantitative Finance 13 (5): 795–818.
  • Barunik, Jozef, and Ladislav Kristoufek. 2010. “On Hurst Exponent Estimation Under Heavy-Tailed Distributions.” Physica A: Statistical Mechanics and Its Applications 389 (18): 3844–3855.
  • Batten, Jonathan A., Harald Kinateder, and Niklas Wagner. 2014. “Multifractality and Value-at-Risk Forecasting of Exchange Rates.” Physica A: Statistical Mechanics and Its Applications 401: 71–81.
  • Buonocore, Riccardo J., Tomaso Aste, and T. Di Matteo. 2017. “Asymptotic Scaling Properties and Estimation of the Generalized Hurst Exponents in Financial Data.” Physical Review E 95: 042311.
  • Buonocore, Riccardo J., Tomaso Aste, and T. Di Matteo. 2016. “Measuring Multiscaling in Financial Time-Series.” Chaos, Solitons & Fractals 88: 38–47.
  • Buonocore, R. J., G. Brandi, R. N. Mantegna, and T. Di Matteo. 2019. “On the Interplay Between Multiscaling and Stock Dependence.” Quantitative Finance 20 (1): 133–145.
  • Calvet, Laurent E., and Adlai J. Fisher. 2002. “Multifractality in Asset Returns: Theory and Evidence.” Review of Economics and Statistics 84 (3): 381–406.
  • Calvet, Laurent E., and Adlai J. Fisher. 2004. “How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes.” Journal of Financial Econometrics 2 (1): 49–83.
  • Calvet, Laurent E., Adlai J. Fisher, and Benoit B. Mandelbrot. 1997. “Large Deviations and the Distribution of Price Changes.” Cowles Foundation Discussion Papers 1165. Cowles Foundation for Research in Economics, Yale University.
  • Chakraborti, Anirban, Ioane Muni Toke, Marco Patriarca, and Frédéric Abergel. 2011. “Econophysics Review: I. Empirical Facts.” Quantitative Finance 11 (7): 991–1012.
  • Clauset, Aaron, Cosma Rohilla Shalizi, and Mark E. J. Newman. 2009. “Power-Law Distributions in Empirical Data.” SIAM Review 51 (4): 661–703.
  • Cont, Rama. 2001. “Empirical Properties of Asset Returns: Stylized Facts and Statistical Issues.” Quantitative Finance 1 (2): 223–236.
  • Corbetta, Alessandro, Vlado Menkovski, Roberto Benzi, and Federico Toschi. 2021. “Deep Learning Velocity Signals Allows to Quantify Turbulence Intensity.” Science Advances 7 (12): eaba7281.
  • Danielsson, Jon, and Jean-Pierre Zigrand. 2006. “On Time-Scaling of Risk and the Square-Root-of-Time Rule.” Journal of Banking & Finance 30 (10): 2701–2713.
  • Di Matteo, T. 2007. “Multi-Scaling in Finance.” Quantitative Finance 7 (1): 21–36.
  • Di Matteo, T., Tomaso Aste, and Michel M. Dacorogna. 2003. “Scaling Behaviors in Differently Developed Markets.” Physica A: Statistical Mechanics and Its Applications 324 (1): 183–188.
  • Di Matteo, T., Tomaso Aste, and Michel M. Dacorogna. 2005. “Long-Term Memories of Developed and Emerging Markets: Using the Scaling Analysis to Characterize Their Stage of Development.” Journal of Banking & Finance 29 (4): 827–851.
  • Eom, Cheoljun, Taisei Kaizoji, and Enrico Scalas. 2019. “Fat Tails in Financial Return Distributions Revisited: Evidence from the Korean Stock Market.” Physica A: Statistical Mechanics and Its Applications 526: 121055.
  • Fukasawa, Masaaki, Tetsuya Takabatake, and Rebecca Westphal. 2019. “Is Volatility Rough?” arXiv preprint arXiv:1905.04852.
  • Gatheral, Jim, Thibault Jaisson, and Mathieu Rosenbaum. 2018. “Volatility is Rough.” Quantitative Finance 18 (6): 933–949.
  • Gençay, Ramazan, Michel Dacorogna, Ulrich A. Muller, Olivier Pictet, and Richard Olsen. 2001. An Introduction to High-Frequency Finance. San Diego: Elsevier.
  • Hurst, Harold Edwin. 1956. “Methods of Using Long-Term Storage in Reservoirs.” Proceedings of the Institution of Civil Engineers 5 (5): 519–543.
  • Jiang, Zhi-Qiang, Wen-Jie Xie, Wei-Xing Zhou, and Didier Sornette. 2019. “Multifractal Analysis of Financial Markets: A Review.” Reports on Progress in Physics 82 (12): 125901.
  • Kantelhardt, Jan W., Stephan A. Zschiegner, Eva Koscielny-Bunde, Shlomo Havlin, Armin Bunde, and H. Eugene Stanley. 2002. “Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series.” Physica A: Statistical Mechanics and Its Applications 316 (1): 87–114.
  • Katsev, Sergei, and Ivan L'Heureux. 2003. “Are Hurst Exponents Estimated from Short or Irregular Time Series Meaningful?” Computers & Geosciences 29 (9): 1085–1089.
  • Kolmogorov, Andrey Nikolaevich. 1962. “A Refinement of Previous Hypotheses Concerning the Local Structure of Turbulence in a Viscous Incompressible Fluid at High Reynolds Number.” Journal of Fluid Mechanics 13 (1): 82–85.
  • Kristoufek, Ladislav. 2010. “Long-Range Dependence in Returns and Volatility of Central European Stock Indices.” Bulletin of the Czech Econometric Society 17: 50–67.
  • Lee, Hojin, Jae Wook Song, and Woojin Chang. 2016. “Multifractal Value at Risk Model.” Physica A: Statistical Mechanics and Its Applications 451: 113–122.
  • Lillo, Fabrizio, and J. Doyne Farmer. 2004. “The Long Memory of the Efficient Market.” Studies in Nonlinear Dynamics & Econometrics 8 (3): 1–1.
  • Livieri, Giulia, Saad Mouti, Andrea Pallavicini, and Mathieu Rosenbaum. 2018. “Rough Volatility: Evidence from Option Prices.” IISE Transactions 50 (9): 767–776.
  • Løvsletten, O., and M. Rypdal. 2012. “Approximated Maximum Likelihood Estimation in Multifractal Random Walks.” Physical Review E 85: 046705.
  • Lux, Thomas. 2004. “Detecting Multi-Fractal Properties in Asset Returns: The Failure of the Scaling Estimator.” International Journal of Modern Physics C 15 (04): 481–491.
  • Lux, Thomas, and Michele Marchesi. 1999. “Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market.” Nature 397 (6719): 498–500.
  • Mandelbrot, Benoit B. 1963. “The Variation of Certain Speculative Prices.” The Journal of Business 36 (4): 394–419.
  • Mandelbrot, Benoit. 1967. “The Variation of Some Other Speculative Prices.” The Journal of Business40 (4): 393–413.
  • Mandelbrot, Benoit B.. 2013. Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E. New York: Springer.
  • Mandelbrot, Benoit B., Adlai Fisher, and Laurent E. Calvet. 1997. “A Multifractal Model of Asset Returns.” Cowles Foundation Discussion Papers 1164. Cowles Foundation for Research in Economics, Yale University.
  • Mantegna, Rosario N., and H. Eugene Stanley. 1995. “Scaling Behaviour in the Dynamics of an Economic Index.” Nature 376 (6535): 46–49.
  • Mantegna, Rosario N., and H. Eugene Stanley. 1999. Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge: Cambridge University Press.
  • Muzy, Jean-François, Emmanuel Bacry, and Alain Arneodo. 1991. “Wavelets and Multifractal Formalism for Singular Signals: Application to Turbulence Data.” Physical Review Letters 67 (25): 3515–3518.
  • Muzy, Jean-François, Emmanuel Bacry, and Alain Arneodo. 1993. “Multifractal Formalism for Fractal Signals: The Structure-Function Approach Versus the Wavelet-Transform Modulus-Maxima Method.” Physical Review E 47 (2): 875–884.
  • Scalas, Enrico, and Kyungsik Kim. 2006. “The Art of Fitting Financial Time Series with Levy Stable Distributions.” arXiv preprint physics/0608224.
  • Sornette, Didier, Yannick Malevergne, and Jean-François Muzy. 2003. “What Causes Crashes?” Risk (Concord, NH) 16: 67–71.
  • Takaishi, Tetsuya. 2020. “Rough Volatility of Bitcoin.” Finance Research Letters 32: 101379.
  • Valsamis, Epaminondas Markos, Henry Husband, and Gareth Ka-Wai Chan. 2019. “Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare.” Computational and Mathematical Methods in Medicine 2019 (3478598): 1–7.
  • Van Atta, C. W., and W. Y. Chen. 1970. “Structure Functions of Turbulence in the Atmospheric Boundary Layer over the Ocean.” Journal of Fluid Mechanics 44 (1): 145–159.
  • Virkar, Yogesh, and Aaron Clauset. 2014. “Power-Law Distributions in Binned Empirical Data.” The Annals of Applied Statistics 8 (1): 89–119.
  • Wang, Jying-Nan, Jin-Huei Yeh, and Nick Ying-Pin Cheng. 2011. “How Accurate is the Square-Root-of-Time Rule in Scaling Tail Risk: A Global Study.” Journal of Banking & Finance 35 (5): 1158–1169.
  • Weron, Rafał. 2001. “Levy-Stable Distributions Revisited: Tail Index > 2 Does Not Exclude the Levy-Stable Regime.” International Journal of Modern Physics C 12 (2): 209–223.
  • Yue, Peng, Hai-Chuan Xu, Wei Chen, Xiong Xiong, and Wei-Xing Zhou. 2017. “Linear and Nonlinear Correlations in the Order Aggressiveness of Chinese Stocks.” Fractals 25 (5): 1750041.