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questions for statistics experts.
what is, consensus wise, the
current best suitable canned prob. distribution function
for modeling price time series, specifically
risk or return distribution?
anybody?
some notes here.
it is well known assumption that return
distribution is peaked ( trendless )
and fat tailed ( trending ) resulting in
combined peaked / fat tail distr.
vs normal / lognormal
however return distributions are not
the same as noise / risk distribution.
noise ( untradable price fluctuation )
always has only positive ( not both )
value relative to current direction of the price movement
( ie deviation ).
on a standard "departure from normality"
plot on typical price time series range distribution
one can see the tails.
transforming the data into log form ( log returns ) and
doing the normality test on lognormal data yields a better result,
however the fat tails are still there as usual,
meaning lognormal distribution is certainly a close fit but not
the perfect fit.
lognormal dist as well as gamma based distributions are the
most commonly used. however parameter estimation
for gamma based distributions is hairy ...
so i am looking for a consensus of what
might be a good approximation fit of the above type
empirical distributions with one of two parms max, simple...
there is great variety of opinions out there and there
is no theoretical backing on any of those as of YET.
*another important note i make is that
since noise or *market friction ( short term ) is the result
of two ( or four ) random ( lognorm )
processes, meaning supply and demand fluctuations
( buying and selling )... therefore short term noise distribution
should be modeled based on those assumptions
( additive random changes ) where as longer
term should be modeled based on the cumulative
changes in the resulting shorter term distributions?
Rayleigh, Weilbull?
Levy type distributions?
student ???
other, subexponential distributions???
hyperbolic or logistic type distributions???
generalized pareto (seems to be the fad now )?
bilo.
ps. i need a distribution fit with simple parameter
estimates to model noise ( risk ) in my system...
if i can't find one i'll have to continue to use
the jerry rigged trimmed lognorm :-) so, please help.
***also i really would like to work with the ( pdf ) function
expert on developing the custom one. i have pretty
good idea in mind what is needed, see * and
e-mail back if interested.
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