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Walter:
The definition was a little over my head, but I want to learn. I recall
reading an article by Mandelbrot where he discussed S&P500 returns
distributions showing leptokurtosis (maybe it was his recent Scientific
American article) and how portfolio management rules assuming Normal
distribution were flawed.
Have you found a practical way to adapt money management techniques to take
this (potentially costly) distortion into account? I guess Optimal f based
on empirical data would more or less take this into account.
I would appreciate that Economics Notes article, and any book suggestions
would be appreciated, too.
Thanks.
P.S. I was denied access to the prola.aps.org site, but the "hypersonic
fractals" site was pretty nifty. After watching "Enemies of the State" last
night, though, I half-expected to see a tiny satellite image of my house
appear :)
----- Original Message -----
From: Walter Lake <wlake@xxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: June 30, 1999 18:18
Subject: Re: Analysis of high speed data
> Hi Glen
>
> More stochastic processes.
>
> "TLF" = Stochastic process with ultraslow convergence to a Gaussian: The
> truncated Lévy flight
> http://prola.aps.org/abstract/PRL/v73/p2946_1
>
> From page 229: The work of Mandelbrot encouraged the development of "...
the
> stable family of distributions (also known as Paretian, Pareto-Levy, Levy
> flights and products of anomalous diffusion) has been a popular choice
among
> researchers for capturing the leptokurtosis - the fat tails and high
peaks -
> that characterizes most financial return distributions. ..."
>
> This is not adding more data to a fill out a normal distribution.
>
> My trader friends are constantly harassing me re the wonderfullness of
> non-Gaussian and time series data etc. Now I can adopt a more balanced
> approach with some specificity to my trading time frame. Using Excel I can
> plot kurtosis charts in shorter time frame bins for seasonality, etc to
give
> me some direction re fat tails Vs central distribution analysis.
>
> Hope that I answered your questions. Will try to track down Mandelbrot's
> article in Economic Notes 1997 and send it to you.
>
> For something fun after a hard day at the screen try ...
> http://www.lynx.ch/Contacts/~/ThomasM/hyper.htm
>
> Best regards
>
> Walter
>
>
>
> ----- Original Message -----
> From: Glen Wallace <gcwallace@xxxxxxxx>
> To: <metastock@xxxxxxxxxxxxx>
> Sent: Wednesday, June 30, 1999 1:29 PM
> Subject: Re: Analysis of high speed data
>
>
> > Walter:
> >
> > Can you please define/explain "TLF processes"? Is this a mathmatical
> > "fitting" of a non-Gaussian distribution into a Normal (ie. bell curve)
> > distribution or is it a "natural" normalization as more data is added?
> >
> > Thanks.
> >
> >
> > ----- Original Message -----
> > From: Walter Lake <wlake@xxxxxxxxx>
> > To: Metastock bulletin board <metastock@xxxxxxxxxxxxx>
> > Sent: June 30, 1999 05:33
> > Subject: Analysis of high speed data
> >
> > > The following from "Financial Markets Tick By Tick" page 248 suggests
an
> > > answer to the confusion surrounding Gaussian Vs non-Gaussian analysis
in
> > > backtesting:
> > >
> > > "... this means that investors with horizons of one month or longer
face
> > > Gaussian risks and that conventional risk management and asset pricing
> is
> > > applicable. On the other hand, investors at shorter horizons will face
> > > non-Gaussian fat-tailed distribution and must therefore use
> high-frequency
> > > data {defined as 30 minute bars} and non-Gaussian probability tools
> (e.g.,
> > > fat-tail estimators, rare event analysis) to quantify their risks.
..."
> > >
> > > As the time periods become longer for the data {i.e., end of day,
> weekly,
> > > monthly} TLF processes converge Non-Gaussian distributions to
Gaussian
> > > distributions {i.e., from fat tails to higher peaked central
> > distributions}.
> > >
> > > "... These conclusions agree with conventional wisdom and practice ...
> and
> > > suggest that high-frequency data analysis is of little value {in
system
> > > testing} to long-term investors. ..."
> > >
> > > They go on to describe the clear seasonality that exists within the
> > > different trading time periods.
> > >
> > > Therefore, the analysis and the seasonality and the trading rules are
> time
> > > period specific to the individual trader. You can pick your time frame
> and
> > > use the appropriate analysis without being confused by the
requirements
> of
> > > other time periods.
> > >
> > > Best regards
> > >
> > > Walter
> > >
> > >
> >
> >
>
>
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