For my own learning I have been following the guide here. It is highly instructive.
Implementing this in R I was able to reproduce the authors results on the data sets provided within some acceptable amount of error. However I noticed something funny. The data seems adjust up by exactly 0.50.
For a GBM process I got a value of approximately 1. The author of the website linked encounters nearly the same thing evaluating the raw Alcoa price series. This is wrong, obviously, since a GBM should have a value near 0.5.
There also seems to be a similar bias in the other data sets, and I have found generating a mean reverting data set results in a value in the .7x range, again obviously biased up almost 0.5.
This confused me because my math is correct per the website. Digging around I've stumbled on this example website implementing it. In there the author clearly indicates H is found by dividing the slope of the regression results by 2. Magically, my H is corrected using the same technique.
So this leaves me quite confused.
- Why does the author of the bearcave not divide their H by 2?
- What is the purpose of this division? What is the justification for it magically fixing my math?