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Hurst exponent estimation from short time series

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Abstract

Fractal investigation of time series is very complex for several reasons. Due to the existence of fully continuous model, on which the majority of conventional methods are based, the quality of Hurst exponent estimate is often influenced by the number of input data and its sampling rate. In this work, we present a novel approach of unbiased Hurst exponent estimate that is suitable especially for short time series. The crucial idea is deriving the discrete fractional Brownian bridge and its statistical properties that can be subsequently used for model parameter estimation. For the verification and demonstration of efficiency of the method, several generators of fractional Gaussian noise are presented and tested.

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Acknowledgements

The paper was created with the support of the Grant SGS14/208/OHK4/3T/14 as Student Grant Competition at the Czech Technical University in Prague.

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Authors and Affiliations

  1. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, Prague, Czech Republic

    Martin Dlask & Jaromir Kukal

Authors
  1. Martin Dlask
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  2. Jaromir Kukal
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Corresponding author

Correspondence to Martin Dlask.

Appendices

Appendix A: MATLAB code of fractional Brownian bridge

The following code provides the calculation of the dfBB (Xk) and fBB (Mk) of the given time series x.

figure a

Appendix B: MATLAB code of autocorrelation function of dfBB

The following code provides the calculation of the mth autocorrelation coefficient of theoretical dfBB constructed from the bridge of length N and Hurst coefficient H.

figure b

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Dlask, M., Kukal, J. Hurst exponent estimation from short time series. SIViP 13, 263–269 (2019). https://doi.org/10.1007/s11760-018-1353-2

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