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A hurst exponent, H, between 0 to 0.5 is said to correspond to a mean reverting process (anti-persistent), H=0.5 corresponds to Geometric Brownian Motion (Random Walk), while H >= 0.5 corresponds to a process which is trending (persistent). The hurst exponent is limited to a value between 0 to 1, as it corresponds to a fractal dimension between 1 and 2 (D=2-...

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The corresponding process would be fractional brownian motion (see here) It is parametrized by the Hurst Exponent. On the referenced site you find a link to some matlab code for simulating realizations of fractional BM. If you want to see some fractional Gaussian Noise in action (Matlab) you can do so here. Further more you might want to look into ...

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I don't believe it means they are efficient. It could only imply that your sample has no persistence (notice I'm not using the term auto-correlation) in the returns, if you did use returns instead of prices. Evidence of EMH via the Hurst exponent is an extrapolation that you cannot make. It just says you cannot reject the null regarding this test. There are ...

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A detailed description of the Hurst Exponent can be found here. A further (rather short search of Google) turned up this site claiming to provide an Excel Workbook with, among other things, Hurst Exponent estimation.

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The Hurst value can be coded to plot values >1. An example of how to tame Hurst values >1 http://www.ual.es/~jgarcia/index_archivos/HURST.pdf Following Weron, once (2) is calculated, the Hurst exponent H will be 0.5 plus the slope of (R/S)n −E(R/S)n. However, if we calculate this modified R/S analysis in this way, results show a Hurst exponent, for some ...

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As you suggest, in the case of non-stationary time series, the Hurst exponent is not suitable to measure the time seires persistence for the reasons you cited in the question. Particularly, when $H(q)$ is a non-linear function of q, as in the non-stationary time-series case, the time-series has to be analysed as it is a multi-fractal system (to deal this ...

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