Multifractal analysis of volatility for detection of herding and bubble: evidence from CNX Nifty HFT

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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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    • 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