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Ian MacAuslan wrote:
> ...For example, what exactly is a "fractally-derived moving average"?
I never heard of that, but I would implement it as an exponential moving
average with the decay factor proportional to the fractal dimension. The
fractal dimension of a market decreases when the market is trending, so
you'd normally want the moving average to respond more quickly with a
lower decay factor.
> I've read fractals can be used as an alternative to using a dominant
> cycle length in a Moving Average. Somewhere else, I read it provides a
> good alternative to ADX.
If you plot the fractal dimension and ADX and dominant cycle length
together, they look remarkably similar, with fractal dimension being an
inverted approximation of the other two. ADX and cycle length increas
when a trend forms, while fractal dimension decreases.
> I can understand if a cycle length function
> returns "22", it's saying that the dominant cycle length is 22- bars
> long. But if a fractal function returns "1.4" --I don't know what to
> make of that.
In any adaptive strategy or indicator, one generally has the adaptive
factor (dominant cycle, fractal dimension, whatever) multiplied by some
value that is adjustable for optimization purposes.
> Maybe because I don't know how a fractal 'function' in EasyLanguage is
> calculated, I can't quite get the connection between snowflakes (as an
> example of infinitely duplicating patterns recurring on ever-smaller (or
> bigger) scales -- and trading a 5-minute bar chart!
The fractal dimension of snowflakes can be measured using a log ratio of
lengths along the edges. For normal objects this results in integer
dimensions. For fractal objects it results in non-integer dimensions.
There are algorithms that calculate fractal dimension of a time series
such as a market.
Hurst Exponent is another way of expressing fractal dimension. If the
dimension is D and Hurst Exponent is H, then H=2-D or D=2-H.
-Alex
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