# Tag Info

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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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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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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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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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The article that you linked mentioned several statistical tests, that approach the question from different angles. However, you should know that bid-ask bounce is not significant if you're looking at daily data on liquid (heavily traded) financial instruments.

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@vanguard2k I haven't exactly been able to satisfy myself with the derivation of the original code, but I have been able to do the next best thing. I've looked at the source of the code, which is QuantStart which credits Dr Tom Starke, which uses a slightly different code and also credits Dr Ernie Chan. I've then gone to Dr Chan's blog and used his ...

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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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I am unaware of the notation in this case but I am still trying to make sense of it. (maybe someone can jump in with an edit?) Here's what I have got: There is the notion of quadratic variation out there that could apply here. You can also think about it as a scalar product (which is the same). You can see that the notation here is rather sloppy, because $\... 2 Hurst exponents are most often used in identifying trends in time series. It's been quite a while, but I read this book years ago and this sort of thing is addressed therein (albeit, in a somewhat superficial manner as typical for any trading-centric modeling). Might be worth checking this out. https://www.amazon.com/Chaos-Order-Capital-Markets-... 2 I think the given python code snippet is composed according to the following steps: $$var(\tau) = \left< |z(t+\tau)-z(t)|^2 \right> \thicksim \tau^{2H}$$ $$\Rightarrow var(...)\thicksim \tau^{2H}$$ $$\Rightarrow std(...) \thicksim \tau^{H}$$ \... 1 The first thing you should ask concerns the amount of information contained in your estimator of the Hurst exponent. Let's say you approach this problem from the perspective of frequentist statistics. No matter how you compute the Hurst exponent, the fact of the matter is that it is a statistic (i.e., a function of the data) and is thus subject to sampling ... 1 I fail to understand how this code works too. In the past, I have used this matlab implementation for the generalized hurst exponent calculation and it was quite reliable. Recently someone has translated this into python, but I haven't tested this yet. Hope that helps. 1 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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