![]() ![]() Smaller and larger values of H indicate stronger mean-reversion and trending, respectively. H is a number between 0 and 1, with H 0.5 indicating a trending time series and H = 0.5 indicating a random walk. ![]() ![]() The Hurst exponent, H, measures the long-term memory of a time series, characterising it as either mean-reverting, trending or a random walk. Net framework to complement our skills in R, C and MATLAB, so expect to see more from us using these tools. We are currently building our skills in both Python and the Microsoft. In this post, we perform the analysis in Python, which is something of a departure from tradition for Robot Wealth. Hopefully we will draw some conclusions around if, when and how we might apply the very attractive theory of Hurst in a manner that is practical to systematic traders. The purpose of this post is to delve into the algorithm behind the calculation of Hurst in an attempt to understand this very question. In the last post, we noted that Hurst gives different results depending on how it is calculated this begs the question of how to choose a calculation method intelligently so that we avoid choosing arbitrary parameters. But as is usually the case when we apply such tools to the financial domain, it isn’t quite that straightforward. It would be great if we could plug some historical time series data into the Hurst algorithm and know whether we expect the time series to mean revert or trend. Even if you have read this post previously, it is worth checking out again as we have updated our method for calculating Hurst and believe this new implementation is more accurate. For a brief introduction to Hurst, including some Python code for its calculation, check out our previous post. What if you had a tool that could help you decide when to apply mean reversion strategies and when to apply momentum to a particular time series? That’s the promise of the Hurst exponent, which helps characterise a time series as mean reverting, trending, or a random walk. ![]()
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