Following up my earlier post on fractional dimensions, I wrote a Python script to automate the technique. It does the measurements on various scales, runs the regression, and produces a chart. This will allow me to analyze more stocks, and over varying timeframes. It also surfaced a computational problem that will be important for developing an indicator.

Shown here is the result for AAPL daily closes in 2016. It matches, approximately, my hand calculation from before – and with a higher R-square.

The computational problem is that, when you are measuring over scale *S*, there are actually *S* distinct series to measure. For example, when *S = 2*, you can measure across all the even-numbered observations, or all the odd ones. The two results will be different, making any kind of trailing indicator erratic. Plus, it seems like a waste of good data.

So, as you can see from the code, I take all the measurements of scale *S*, average them, and then multiply by *N/S*, where *N* is the total number of observations. This gives an idealized *L(S)* using all the data.

The practical problem is that the Hausdorff dimension describes the entire sample period, like a *Volume by Price* chart, and it yields a single number. In theory, this tells how much noise to expect on lower timeframes, between moves of a given size on the higher timeframe. That would be handy to know when setting stops.

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