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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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