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I've grouped and rearranged all my responses into one posting:
>>sure, the math's flawed, but the concept is valid.<<
It's only valid when you are adding apples to apples.
>>but does that make the calculation useless? I'm no expert at applying the PFE, but it seems to me that you could use relative values of the PFE. E.g. compare the current value to the N-period average, or whatever. That way the absolute value of the function isn't a problem. Or is the concept so flawed as to be unusable?<<
It's not the absolute value that's the problem, but the nonlinear interaction between the apples and oranges. To take an extreme example, suppose you are applying it to a stock whose trading range for the month hovers between $5 and $20. The time series at the $20 level needs to behave for more efficiently than at the $5 level just to get the same PFE value, and that's the problem. As price gets even smaller, efficiency is biased upward, eventually converging to PFE = N/(N-1), an efficiency greater than 1, regardless of what the price action is doing!
In the other direction, if you take the limit of the PFE algorithm as price becomes very large relative to the bar count, the formula converges to the Kaufman efficiency ratio (KER). In other words, removing the constants from PFE gives you KER, which is scale invariant. KER very cleanly and correctly compares actual price action against ideal price action. But neither KER or PFE is really analyzing the fractal nature of the time series. They are simply comparing the total price excursion of two trends, one real and one ideal.
>> i like the idea of measuring price movement rather than price trend, it's a more accurate model of market behavior.<<
I agree.
>> i think a better approach would be to derive the "static" hurst exponent for whatever market or time frame we trade,<<
Yes. But it's not trivial to calculate. The only software I now that provides the Hurst exponent is by Bloomberg. Any others?
Mark Jurik
Jurik Research
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