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Jeff,
Amazing how some of this stuff comes back, I had forgotten about
leptokurtosis - sounds like a disease doesn't it.
I did a significant study in this area on the Brent Oil market in about
93/4. I suspect I threw it into the bin when I left Shell. I havn't picked
up Peters' book in a number of years either.
I think I'm going to have to take some time out and fiddle with the
equations. I'd forgotten how much I enjoyed this area.
As regards yr. other posting, I don't think you are being confrontational at
all. I completely agree. I guess, that my sense of it is that an excellent
fundamental analyst will always outperform an excellent chartist. What will
let him down will be the number of stocks he can manage. Thus an average
chartist will tend to out perform a good analyst. At the limit, I see a
black box outperforming the individual purely because of scope and freedom
from emotion.
On your other point regarding data, I couldn't agree more. If you look at a
chart on the screen, one can ignore the bad tick. In a network, you can't.
Cleanliness of data is paramount.
I must confess I've given up and what little success I've had tends to come
from technical analysis rather than NNs. However, I would still commend
using a GA to search for indicator settings. It's extremely fast.
Take care
DJ
----- Original Message -----
From: "Jeff Haferman" <haferman@xxxxxxxxxxxxxxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: Wednesday, February 07, 2001 4:00 PM
Subject: Re: Artificial Intelligence, expert and neural
> David Jennings wrote:
> >
> >As an aside, whilst they fit markets quite well, different parameters are
> >required over different time frames. Thus the question to you guys is: if
> >this is corect (and I believe it to be) it flatly ontradicts any fractal
> >market hypothesis. Any assistance would be helpful.
> >
>
> My opinion is that it doesn't contradict any FMH. I'm cheating
> here and looking at Edgar Peter's "Chaos and Order..."
> specifically his Eq. (9.2). If you don't have the book,
> this is an equation for a Pareto-Levy distribution, which has
> 4 characteristic parameters. [I would reproduce the Eq here,
> but it would take some work!] Call the parameters A, B, C, and D.
>
> Peters states that a normal dist'n results when A=2, B=0, C=1,
> and D=1. A fat-tailed, skewed-to-the-right (i.e. leptokurtotic)
> dist'n results when A is between 1 and 2, and B approaches 1.
> It turns out A is actually the fractal dimension of the dist'n.
>
> Now, what is the mean of this second distribution? It depends
> on the time frame! For daily prices, if the mean is M, then
> for 5-day returns the mean is 5*M. So, this is a case where
> the distribution of the returns has a time-dependent parameter,
> but the distribution is fractal.
>
> So, to apply this to GARCH, it really comes down to this:
> is the fractal dimension of the distribution independent of
> the time frame? Any other parameters of the distribution
> do not need to be independent of the time frame.
>
> Jeff
>
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