Multifractal analysis of volatility for detection of herding and bubble: evidence from CNX Nifty HFT
-
Author(s)Bikramaditya GhoshLink to ORCID Index: https://orcid.org/0000-0003-0686-7046
,
Emira KozarevićLink to ORCID Index: https://orcid.org/0000-0002-5665-640X
-
DOIhttp://dx.doi.org/10.21511/imfi.16(3).2019.17
-
Article InfoVolume 16 2019, Issue #3, pp. 182-193
- Cited by
- 998 Views
-
303 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
This study delves into the herding and bubble detection in the volatility domain of a capital market underlying. Furthermore, it focuses on creating heuristics, so that common investors find it relatively easy to understand the state of the market volatility. Hence, it can be termed that this study is focused on the specific financial innovation regarding bubble and herding detection coupled with investor awareness. The traces of possible volatility bubble emerge when it is positioned against its own lags (both lag1 and lag2). The volatility trigger indicated clear traces of herding and an embedded parabola function. Continuous and repetitive parabola function hinted at a subtle presence of “fractals”. Firstly, the detrended fluctuation analysis has been used with its multifractal variant. Secondly, the regularized form of Hurst calculation and analysis have been used. Both tests reveal the traces of nascent bubble formation owing to prominent herding in CNX Nifty HFT environment. They also indicate a clear link with Hausdorff topological patterns. These patterns would help to create heuristics, enabling investors to be aware of possible bubble and herd situations.
- Keywords
-
JEL Classification (Paper profile tab)B16, B23, C52
-
References19
-
Tables3
-
Figures10
-
- Figure 1. Multifractal, monofractal, and white noise like time series
- Figure 2. Cubic, quadratic, and linear detrending
- Figure 3. Root mean square (RMS)
- Figure 4. Hurst exponent
- Figure 5. qth-order RMS for different time series
- Figure 6. qth-order Hurst exponent for different time series
- Figure 7. The multifractal spectrum of time series
- Figure 8. Estimation of the Hurst exponent
- Figure 9. Douady rabbit
- Figure 10. Dendrite Julia set
-
- Table 1. Zone of the Hurst exponent
- Table 2. GHE output
- Table 3. Fractal geometry and topology connection
-
- Hausdorff, F. (1918). Dimension und ausseres Mass. Mathematische Annalen, 79(1-2), 157-179.
- Hurst, H. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116(1), 770-799.
- Ihlen, E. A. F. (2012). Introduction to multifractal detrended fluctuation analysis in Matlab. Frontiers in Physiology, 141(3).
- Jiang, Z.-Q., Xie, W.-J., Zhou, W.-X., & Sornette, D. (2018). Multifractal analysis of financial markets.
- Kantelhardt, J. W. (2008). Fractal and Multifractal Time Series (59 p.).
- Kantelhardt, J. W., Zschiegner, S. A., Koschielny-Bunde, E., Havlin, S., Bunde, A., & Stanley, H. E. (2002). Multi-fractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications, 316(1-4), 87-114.
- Los, C. A., & Lipka, J. M. (2003). Long-Term Dependence Characteristics of European Stock Indices. SSRN Electronic Journal, 1-40.
- Mandelbrot, B. (1999). A Multifractal Walk down Wall Street. Scientific American, 280(2), 70-73.
- Mandelbrot, B. B. (1963). The Variation of Certain Speculative Prices. The Journal of Business, 36(4), 394-419.
- Mandelbrot, B. B. (1977). Fractals: form, chance and dimension (International Business Machines, Thomas J. Watson Research Center) (XVI). San Francisco: W.H. Freeman and Co..
- Mandelbrot, B. B., Fisher, A. J., & Calvet, L. (1997). A Multifractal Model of Asset Returns (Working Papers – Yale School of Management’s Economics Research Network, 1).
- Redelico, F. O., & Proto, A. N. (2012). Empirical fractal geometry analysis of some speculative financial bubbles. Physica A: Statistical Mechanics and its Applications, 391(21), 5132-5138.
- Riedi, R. H. (1999). Introduction to Multifractals. Houston.
- Safari, A., & Seese, D. (2009). Non-parametric estimation of a multiscale CHARN model using SVR. Quantitative Finance, 9(1), 105-121.
- Suárez-Garcíaa, P., & Gómez-Ullate, D. (2014). Multifractality and long memory of a financial index. Physica A: Statistical Mechanics and its Applications, 394, 226-234.
- Thompson, J. R., & Wilson, J. R. (2016). Multifractal detrended fluctuation analysis: Practical applications to financial time series. Mathematics and Computers in Simulation, 126, 63-88.
- Vardhini, P., Punitha, N., Navaneethakrishna, M., & Ramakrishnan, S. (2018). Multifractal Analysis of Term and Preterm Uterine EMG Signals Using Wavelet Leaders. In IEEE Life Sciences Conference (LSC) (pp. 271-274).
- Wang, W., Liu, K., & Qin, Z. (2014). Multifractal Analysis on the Return Series of Stock Markets Using MF-DFA Method. In 15th International Conference on Informatics and Semiotics in Organisations (ICISO, 2014) (pp. 107-115). Shanghai: Springer.
- Watkins, N. W., & Franzke, C. (2017, August). A brief history of long memory: Hurst, Mandelbrot and the road to Road to ARFIMA, 1951–1980. Entropy, 19(9), 437.
-
Identifying explosive behavioral trace in the CNX Nifty Index: a quantum finance approach
Bikramaditya Ghosh ,
Emira Kozarević
doi: http://dx.doi.org/10.21511/imfi.15(1).2018.18
Investment Management and Financial Innovations Volume 15, 2018 Issue #1 pp. 208-223 Views: 2181 Downloads: 5431 TO CITE АНОТАЦІЯThe financial markets are found to be finite Hilbert space, inside which the stocks are displaying their wave-particle duality. The Reynolds number, an age old fluid mechanics theory, has been redefined in investment finance domain to identify possible explosive moments in the stock exchange. CNX Nifty Index, a known index on the National Stock Exchange of India Ltd., has been put to the test under this situation. The Reynolds number (its financial version) has been predicted, as well as connected with plausible behavioral rationale. While predicting, both econometric and machine-learning approaches have been put into use. The primary objective of this paper is to set up an efficient econophysics’ proxy for stock exchange explosion. The secondary objective of the paper is to predict the Reynolds number for the future. Last but not least, this paper aims to trace back the behavioral links as well.
-
Predictability and herding of bourse volatility: an econophysics analogue
Bikramaditya Ghosh ,
Krishna M.C. ,
Shrikanth Rao ,
Emira Kozarević ,
Rahul Kumar Pandey
doi: http://dx.doi.org/10.21511/imfi.15(2).2018.28
Investment Management and Financial Innovations Volume 15, 2018 Issue #2 pp. 317-326 Views: 2069 Downloads: 216 TO CITE АНОТАЦІЯFinancial Reynolds number works as a proxy for volatility in stock markets. This piece of work helps to identify the predictability and herd behavior embedded in the financial Reynolds number (time series) series for both CNX Nifty Regular and CNX Nifty High Frequency Trading domains. Hurst exponent and fractal dimension have been used to carry out this work. Results confirm conclusive evidence of predictability and herd behavior for both the indices. However, it has been observed that CNX Nifty High Frequency Trading domain (represented by its corresponding financial Reynolds number) is more predictable and has traces of significant herd behavior. The pattern of the predictability has been found to follow a quadratic equation.
-
Power law in tails of bourse volatility – evidence from India
Bikramaditya Ghosh ,
M. C. Krishna
doi: http://dx.doi.org/10.21511/imfi.16(1).2019.23
Investment Management and Financial Innovations Volume 16, 2019 Issue #1 pp. 291-298 Views: 1014 Downloads: 148 TO CITE АНОТАЦІЯInverse cubic law has been an established Econophysics law. However, it has been only carried out on the distribution tails of the log returns of different asset classes (stocks, commodities, etc.). Financial Reynolds number, an Econophysics proxy for bourse volatility has been tested here with Hill estimator to find similar outcome. The Tail exponent or α ≈ 3, is found to be well outside the Levy regime (0 < α < 2). This confirms that asymptotic decay pattern for the cumulative distribution in fat tails following inverse cubic law. Hence, volatility like stock returns also follow inverse cubic law, thus stay way outside the Levy regime. This piece of work finds the volatility proxy (econophysical) to be following asymptotic decay with tail exponent or α ≈ 3, or, in simple terms, ‘inverse cubic law’. Risk (volatility proxy) and return (log returns) being two inseparable components of quantitative finance have been found to follow the similar law as well. Hence, inverse cubic law truly becomes universal in quantitative finance.
