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sure, the math's flawed, but the concept is valid. hans tried to carry
the analogy of measuring a coastline (where delta x and delta y = units
of measure, apples = apples) to a time price series (where delta price
and delta time are not equivalent units of measure, apples are not
equal to oranges). it's the same problem we discussed several months
ago with price "velocity" and "momentum."
i think that using pfe "as is" is ok on a relative basis, similar to
the way we use momentum or velocity on a relative basis. i like the
idea of measuring price movement rather than price trend, it's a more
accurate model of market behavior.
but i've got a problem using jurik's fractal dimension....the
adjustable inputs. i can change the inputs and create whatever fiction
i might desire, but may or may not relate to market reality. i
understand that it's a mathematical shortcut to get at the hurst
exponent (fd = 2 - h) which data calculation intensive (r/s analysis),
but i think a better approach would be to derive the "static" hurst
exponent for whatever market or time frame we trade, and then back into
the fractal dimension from the exponent side, adjusting the fd inputs
to get the proper value of h. that seems to me to be preferable to
guessing or optimization. just some thoughts......
TJ
mj wrote:
> > So much for theory. It's flawed. Simply put, Hans was attempting
> > to combine apples and oranges, producing a function that is not
> > scale invariant. The apples and oranges are the two axes
> > themselves: net bar count and net price change, which he combines
> > through mere addition. Yes, the curve goes up and down, but if you
> > convert price in the time series, say from dollars to francs, the
> > function produces different values.
gf replied:
> I see your point, 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?
mj wrote:
> > There's a completely different approach that is mathematically
> > sound. Assume that if the market was a random walk, how would its
> > net change in price vary as a function of the number of bars? The
> > answer is net_price = C x delta_time ^ 0.5, where C is a scaling
> > constant.
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