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Pal, you said earlier "...Statistics is meaningless in the context that you
can come out with statistics to disprove anything." So, I misspoke. You were
talking about disproof, whereas I was speaking of proof (mathematically, one is
1 minus the other). But no matter. Let me go one step further. Suppose the
null hypothesis is A is not equal to B. Put in terms of trading parlance, the
null hypothesis might be when the short MA of C crosses above the long MA of C,
prices will not rise. In order to disprove that hypothesis, I have to try to
prove that A = B (the alternate hypothesis); in other words, I have to prove
that when the short MA of C crosses above the long MA of C, the price rises. So,
I design an experiment (a backtest) to get as much information to prove that A =
B. If I obtain sufficient data to show that A is not equal to B (i.e., the
MA cross does not signal a price rise) and can say so at the 95 or 99%
confidence level, I think I have disproven in a statistical sense the null
hypothesis at some level of confidence PROVIDED my sampling was representative
and the sampling size was sufficiently high to generate the proper amount of
statistical confidence. I will have demonstrated my point with an error of 5% or
1%. And of course, I must first establish that my dataset is normally
distributed, otherwise my 'proof' is faulty. This analysis does not by any means
constitute proof with certainty, which is impossible because one cannot sample
the entire uinverse of data available. It only establishes a degree of
confidence based on a sampling of a limited population of price data and the
inherent error associated with it. Sample size is critical to any statistical
analysis. The higher, the better. That's all statistics does. You may still act
on the MA cross by buying, but you have been warned that if you do, the
probability is very high that you will lose. There are all kinds of other things
I haven't even touched on, such as sampling from a population of correlated
stocks, or sampling only during a bull market, etc., etc. Nothing is certain in
the game of prediction.
Al Venosa
<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
palsanand
To: <A title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Sunday, October 26, 2003 4:55
PM
Subject: [amibroker] Re: solving the
prediction problem
Hi,I was speaking only of absolute proof and it
solely belongs in the realm of physical law or mathematical theorem, not
statistics.Regards,Pal--- In <A
href="">amibroker@xxxxxxxxxxxxxxx, "Al
Venosa" <advenosa@x...> wrote:>
Pal,> > Sorry, but I have to take the side of MarkF2 on this
one. Yes, I agree, you can prove anything you want with statistics, but
only if you use it improperly, which most people who have a vested
interest in something or are not objective in their analysis of an
empirical observation do (understand, I am not accusing you of anything;
I'm just stating a fact). If you use inferential, parametric statistics
on data that are not even close to being normally distributed, you can
prove anything. But your proof is flawed because you have misused a basic
underlying assumption that the particular statistical test was designed to
indicate. You speak of proof being only in the realm of physical law or
mathematical theorem. Perhaps true if you speak of absolute proof.
However, in statistics, all 'proofs' are based on measurement error, and
there is nothing on this planet that can be measured error-free (except
mathematical principles such as the area of a triangle or the Pythagorean
Theorem). In trading, the errors are huge, sometimes infinite, because
price behavior is so variable; so in order to try to 'prove' anything
statistically, you have to minimize that error as much as possible. How
does one minimize error when prices are determined by such a huge universe
of human beings, all with different outlooks on future behavior and all
biased to some degree by their own non-objective views? You can't. You can
only generate probabilities and confidence based on those probabilities,
and that is the heart of statistical analysis. So, statistics is not
meaningless at all and in fact is a very valuable tool in this
complicated trading business of ours. Use it properly, and you will be
rewarded. Use in unwisely, and you will lose big. > > Al
Venosa> ----- Original Message ----- >
From: palsanand > To: amibroker@xxxxxxxxxxxxxxx
> Sent: Sunday, October 26, 2003 3:41
PM> Subject: [amibroker] Re: solving the prediction
problem> > > I do not dispute the usefulness
of statistics, only in the use of it > to prove
something, which anybody who has a good grasp of statistics
> in this planet knows, which apparently you don't.>
> Regards,> >
Pal> --- In amibroker@xxxxxxxxxxxxxxx, "MarkF2"
<feierstein@xxxx> wrote:> > What planet are
you from? Statistics *is* a branch of applied> >
mathematics and, IMHO, the single most useful for trading.>
> > > "Each of us has been doing statistics all his
life, in the sense > that> > each
of us has been busily reaching conclusions based on
empirical> > observations ever since birth." --
William Kruskal > > > > --- In
amibroker@xxxxxxxxxxxxxxx, "palsanand" <palsanand@xxxx>
> wrote:> > > >
> Like I said earlier, Statistics is meaningless in the context
> that > > > you can come out with
statistics to disprove anything. Proof > > >
requires a law or a theorem. Only Mathematics can prove
or> > disprove > > > and that
is one reason it is the greatest of all sciences.> >
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