Multifractal analysis of volatility for detection of herding and bubble: evidence from CNX Nifty HFT
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DOIhttp://dx.doi.org/10.21511/imfi.16(3).2019.17
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Article InfoVolume 16 2019, Issue #3, pp. 182-193
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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.
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JEL Classification (Paper profile tab)B16, B23, C52
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References19
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Tables3
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Figures10
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- 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
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- Table 1. Zone of the Hurst exponent
- Table 2. GHE output
- Table 3. Fractal geometry and topology connection
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- 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.