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Author Topic: 1.5?  (Read 3357 times)
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luuc
Guest
« on: November 13, 2006, 12:57:23 PM »

Quote
A Gaussian random walk has a fractal dimension of exactly 1.5
; But how has this been calculated? huh?

And what does the fractal dimension in the stock market mean?

I have absolutely no idea what the connection is between those two; I'v been trying to find my anwser; but without any results. sad

It would really help me if someone could help me.
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lkmitch
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« Reply #1 on: November 14, 2006, 04:27:21 PM »

Quote
A Gaussian random walk has a fractal dimension of exactly 1.5
; But how has this been calculated? huh?

A random walk is generally the set of points created by starting at some initial point and then randomly "walking" or displacing the point each iteration.  The distribution of the random displacements determines the fractal dimension of the walk.

Quote
And what does the fractal dimension in the stock market mean?

In financial (and other) analyses, one generally creates a time-series representation of the underlying phenomenon (like the price of a given stock over time) and determines the fractal dimension of that dataset.  A larger dimension implies more volatility in the stock (or turbulence, if the data represent have some fluid mechanical representation); a smaller dimension implies a smoother path.

Kerry
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muis
Guest
« Reply #2 on: November 17, 2006, 10:09:15 AM »

The fractal dimension represents the state of the market. A fractal dimension of 1.5 implies an random (unpredictable) market, and hence an random walk with dimension 1.5 implies an unpredictable state of the market.
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heneganj
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« Reply #3 on: April 04, 2007, 10:04:48 PM »

I'm about to do some work trying to predict the stock market!   cheesy  I fear this is a well trodden path.

I wonder what use Fractals could be..  smiley
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lkmitch
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« Reply #4 on: April 05, 2007, 01:02:07 AM »

Mandelbrot says (paraphrasing) that fractals are great for modeling the statistical nature of the market and horrible for making specific predictions.

Remember us when you strike it rich.   smiley
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heneganj
Guest
« Reply #5 on: April 05, 2007, 08:44:31 PM »

Of course!

My task is to try and find correlations between two datasets - both prices of different stocks over time.  If I can find that two datasets are correlated over a specific time window, then the subsequent time window may be used to predict how the stock will move next.  I was going to brute-force scanning through various time windows and ranges of both datasets, and see how each is correlated (I am looking at the Excel function CORREL at the moment), but this looks like a massive task.

There may be some mileage in using fractal dimension of a subrange of a dataset in order to reduce the sheer number of comparisons as it may be fruitless to compare subranges with wildly disparate fractal dimensions.  I say 'may be', this is something I'll have to look into.


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lkmitch
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« Reply #6 on: April 07, 2007, 04:16:05 AM »

CORREL is based on linear correations, yes?  Try it with a Julia orbit for two different (real) c values.  If you can't find a correlation there (when you know what the rules are), I don't think you'll find a useful one in the field.  If might want to restrict your searches to stocks/windows where the fractal dimensions are similar--maybe that implies similar dynamics.
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lycium
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« Reply #7 on: May 09, 2007, 03:33:15 AM »

I'm about to do some work trying to predict the stock market!   cheesy  I fear this is a well trodden path.

I wonder what use Fractals could be..  smiley

see also http://en.wikipedia.org/wiki/Fractomancy
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