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--- Lionel Issen <lissen@xxxxxxxxxxxxxx> wrote:
> What does L2 mean?
>
Sorry, should have explained that. L2 stand for "Lebesgue measureble of
degree 2". In loose terms that means that the functions has finite
energy. So you either sum or integrate the f^2 over all real numbers.
For the sampled versions (which stock prices are) you would take a
finite sample and replicate it infinitely. That's also how fourier
transforms of finite sequences work.
So my original point was that even while stock prices don't meet the
requirments for fourier, the essense remains valid. So it's important
not to get hung up on the trying to rely any "precise" statements about
spectrum and sampling, but rather to look at the information that
fourier gives you as something "close".
I hope that clarifies my original comments. I wasn't meant to be deep,
just an observation about how far to stretch the math.
> -----Original Message-----
> From: owner-metastock@xxxxxxxxxxxxx
> [mailto:owner-metastock@xxxxxxxxxxxxx]On Behalf Of Allan Havemose
> Sent: Monday, February 25, 2002 2:29 PM
> To: metastock@xxxxxxxxxxxxx
> Subject: Re: information frequency vs tradeability
>
>
> Rudolf,
>
> with the risk of sounding like a teacher, I dont believe you have
> your
> facts straight. The most general version of Fourier (incl sampling
> theorem) that I'm aware of requires the underlying function to be L2.
> All the data I've seen on stock prices certainly doesn't indicate
> that
> they are L2. I don't remember where I saw it, but I believe that
> there
> is even research indicating that the variance is ever increasing,
> hence
> no chance of every being L2.
>
> Allan
>
> --- rudolf stricker <lists@xxxxxxxxxxx> wrote:
> >
> > Allan,
> >
> > On Fri, 22 Feb 2002 15:31:48 -0800 (PST), you wrote:
> >
> > >one thing to remember, is that the fourier theory, sampling
> theorem
> > >etc. are not valid on stock price data.
> >
> > Imho, you are simply wrong here. As a basic theorem for discreet
> time
> > series, Fourier's sampling theorem of course is valid also for
> stock
> > price data in the sense of a _necessary_ (not sufficient)
> condition,
> > because it _is_ a piece of essence for all discreet (time) series.
> >
> > >Most of those theorems make
> > >fairly strong assumptions regarding the underlying function and
> > metric.
> >
> > Can you please list some of these assumptions for Fourier's
> sampling
> > theorem, that might not be fulfilled for discreet stock price data
> ?
> >
> > mfg rudolf stricker
> > | Disclaimer: The views of this user are strictly his own.
>
>
> =====
> ---
> Allan Havemose, Ph.D.
> havemose@xxxxxxxxxx
> havemose@xxxxxxxxx
>
> __________________________________________________
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=====
---
Allan Havemose, Ph.D.
havemose@xxxxxxxxxx
havemose@xxxxxxxxx
__________________________________________________
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