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I am trying to estimate the Hurst Exponent for financial data using the R/σ (Rescaled Range) method. I have no authoritative source for this method. All I have are web pages (and we know how accurate those are). Specifically, I've been using the following pages.

https://en.wikipedia.org/wiki/Rescaled_range

https://en.wikipedia.org/wiki/Hurst_exponent

http://www.bearcave.com/misl/misl_tech/wavelets/hurst/

http://analytics-magazine.org/the-hurst-exponent-predictability-of-time-series/

http://www.financialwisdomforum.org/gummy-stuff/hurst.htm

I know that the Hurst Exponent must be between 0 and 1, and I keep getting results that are a little bigger than 1. I have tried to follow the above articles to the letter, and I am at my wit's end trying to find a mistake. I have attached an Excel spreadsheet with my calculations for 64 data points, if you're inclined to look at them.

The page called Data just has the raw data. No need to look at that.

The page called Wikipedia has the following calculation method.

* Divide the 64 points into 8 groups of 8 sets of closing prices C.

* Compute the mean m of each group of 8 closing prices (Column E).

* Compute a mean-adjusted time series (Y = C - m) for each group of 8 closing prices. (Column F).

* Compute the cumulative variate time series Z for each group of 8 mean-adjusted prices (Column G).

* Compute the range R of each group of 8 cumulative variates (Column H).

* Compute the standard deviation σ of each group of closing prices(Column I).

* Compute the rescaled range R/σ of each group (Column J).

* Compute the average of the rescaled ranges E[R/σ] of all groups of size 8 (Cell AH3).

* Repeat all of the above steps for groups of size N = 16, 32, and 64.

* Compute the slope of the regression line for log(N) vs log(E[R/σ]) (Columns AI-AJ).

The result of the last step is supposed to be the estimate of the Hurst Exponent, which I would expect to come out to be about 0.5, give or take. Instead it came out to 1.03.

In the page called FinancialWisdom, I used the method from the last link. That page recommended breaking the data up into subsets with incrementally increasing lengths, so I used N = 8, 16, 24, 32, 40, 48, 56, and 64. Again, no joy.

If anyone can either tell me what I'm doing wrong, or point me to a reference that clearly explains how to do this, I'd be most grateful. Thanks!

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# A Estimation of Hurst Exponent Using Rescaled Range

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