> >
40yahoogroups.com>,
> > Howard B
> > > > <howardbandy@> wrote:
> > > > > >
> > > > > > Hi Brian --
> > > > > >
> > > > > > I use a Hughes satellite connection to
the Internet. It
seems
> > > > that
> > > > > Hughes
> > > > > > appears to Rapidshare as a single user
(which is always
over
> > its
> > > > > limit), so
> > > > > > I am never able to download a Rapidshare
file. If
possible,
> > > > could
> > > > > you
> > > > > > upload the files to the Yahoo AmiBroker
file section?
> > > > > >
> > > > > > Thanks,
> > > > > > Howard
> > > > > >
> > > > > >
> > > > > > On Sat, Feb 7, 2009 at 9:10 PM,
brian_z111 <brian_z111@>
> > wrote:
> > > > > >
> > > > > > > I am using Rapidshare for file
sharing.
> > > > > > >
> > > > > > > Free downloads are available but
they are slower than
paid
> > > > > download
> > > > > > > and limited to 1 download per time
... wait a while and
you
> > can
> > > > > > > download again (still good value for
my customers).
> > > > > > >
> > > > > > >
> > > >
http://rapidshare.com/files/195190948/BinomialMaster_ABVersion.xls
> > > > > > >
> > > > > > > A short ReadMe, to help understand
the file, is at:
> > > > > > >
> > > > > > >
http://zboard.wordpress.com/
> > > > > > >
> > > > > > > I can answer a few questions about
the details in the
file
> > for a
> > > > > > > limited time (while my memory is
fresh) .... post
> > questions, if
> > > > > any,
> > > > > > > via comments at the Zboard.
> > > > > > >
> > > > > > >
> > > > > > > --- In
amibroker@xxxxxxxxxps.com
<amibroker%
40yahoogroups.com><amibroker%
> >
40yahoogroups.com><amibroker%
> > > >
40yahoogroups.com>,
> > > > > > > "brian_z111" <brian_z111@>
wrote:
> > > > > > > >
> > > > > > > > File limits prevented me
uploading the
BinomialSimulation
> > file
> > > > > (s)
> > > > > > > to
> > > > > > > > this group ... 20MB per file. I
will post links to at
> > least
> > > > one
> > > > > > > > example, at the following
temporary site, sometime
this
> > week:
> > > > > > > >
> > > > > > > >
http://zboard.wordpress.com/
> > > > > > > >
> > > > > > > > I will post some basic notes
afterall because the
task of
> > > > > following
> > > > > > > > the Excel sheets would be
beyond anyone without them.
> > > > > > > >
> > > > > > > > The site might live on for a
while after that.
> > > > > > > >
> > > > > > > >
> > > > > > > > --- In
amibroker@xxxxxxxxxps.com <amibroker%
40yahoogroups.com><amibroker%
> >
40yahoogroups.com><amibroker%
> >
> > > >
40yahoogroups.com>,
> > > > > > > "brian_z111" <brian_z111@>
wrote:
> > > > > > > > >
> > > > > > > > > I decided to post the
Binomial Simulation files a
few
> > days
> > > > > > > ago ...
> > > > > > > > I
> > > > > > > > > am not going to announce
the upload so this post is
the
> > > > > > > discussion
> > > > > > > > > link for them (one or more
files will appear at some
> > stage).
> > > > > > > > >
> > > > > > > > > FTR They do predict the eq
dist quite well, for
biased
> > and
> > > > > none
> > > > > > > > > biased 'coins' but there
is one thing about them
that
> > does
> > > > > > > concern
> > > > > > > > > me ... I referenced the
same synthetic trade series
to
> > make
> > > > > the
> > > > > > > > > binomial distribution and
to create the synthetic eq
> > > > > curves ...
> > > > > > > > that
> > > > > > > > > seems a bit incestuous in
some ways.
> > > > > > > > >
> > > > > > > > > On the other hand they
could be full of incorrect
math
> > > > > > > assumptions
> > > > > > > > > cos I got the math off
Wikipedia!
> > > > > > > > >
> > > > > > > > > Guru Brian ;-)
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > --- In
amibroker@xxxxxxxxxps.com<amibroker%
40yahoogroups.com><amibroker%
> >
40yahoogroups.com><amibroker%
> >
> > > > >
40yahoogroups.com>,
> > > > > > > "brian_z111" <brian_z111@>
> > > > > > > wrote:
> > > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > > This is a valid
model as long as stationarity
> > holds ...
> > > > I
> > > > > > > have
> > > > > > > > > > > simulated random
trading 'systems' and
predicted the
> > > > > outcome
> > > > > > > by
> > > > > > > > > > using
> > > > > > > > > > > binomial
probability, that references a
frequency
> > > > > > > distribution
> > > > > > > > of
> > > > > > > > > > the
> > > > > > > > > > > randomly
generated trades, and it predicted the
> > actual
> > > > > equity
> > > > > > > > > > > distributions
extremely well (a lognormal dist
> > appears
> > > > at
> > > > > > > very
> > > > > > > > > high
> > > > > > > > > > > N's).
> > > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > More precisely, I
have simulated trade series,
using
> > the
> > > > > RNG in
> > > > > > > > > > Excel, for random
walks (50/50 systems) and biased
> > > > systems,
> > > > > > > with
> > > > > > > > > > normally distributed
trade series (I used
> > > > > CentralLimitThereom
> > > > > > > to
> > > > > > > > > > create NormDists from
the uniform output of the
> > generator.
> > > > > > > > > >
> > > > > > > > > > I simulated equity
curves, using the synthetic
trades,
> > > > and
> > > > > at
> > > > > > > the
> > > > > > > > > > same time used
BinomialProb to model the predicted
> > > > > distribution
> > > > > > > > of
> > > > > > > > > > the eq curves (I
imagined I was tossing a coin
with
> > > > variable
> > > > > > > > values
> > > > > > > > > > for heads and tails
... of course in trading we
can
> > win
> > > > > lose or
> > > > > > > > > draw
> > > > > > > > > > whereas in my model
we can only win or lose).
> > > > > > > > > >
> > > > > > > > > > You might like to see
the files?
> > > > > > > > > >
> > > > > > > > > > I am bored with that
topic.
> > > > > > > > > >
> > > > > > > > > > I am not a
mathematician ... it might be a load
of old
> > > > > rubbish
> > > > > > > > for
> > > > > > > > > > all I know.
> > > > > > > > > >
> > > > > > > > > > As our discussion
shows .. we can't get any
> > statistical
> > > > > > > certainty
> > > > > > > > > > anywhere in trading
... only approximations and
> > > > > probabilties.
> > > > > > > > > >
> > > > > > > > > > It is just another
approximation, like MCS and
> > involves
> > > > > massive
> > > > > > > > > > number crunching.
> > > > > > > > > >
> > > > > > > > > > I didn't finish it
because I wanted a quick and
dirty
> > > > > method.
> > > > > > > > > >
> > > > > > > > > > The files are rough
as old bags.
> > > > > > > > > >
> > > > > > > > > > I didn't make notes
so even I have a hard time
> > following
> > > > the
> > > > > > > > > > logic ... I had a
look at them the other day I
had to
> > > > start
> > > > > > > > tracing
> > > > > > > > > > the formulas in the
cells to see how I had done
it.
> > > > > > > > > >
> > > > > > > > > > I'll post some of
them in the file section one day
> > (Howard
> > > > > > > > collects
> > > > > > > > > > trading things).
> > > > > > > > > >
> > > > > > > > > > I won't scrub them up
though ... take them or
leave
> > > > them ...
> > > > > > > > sorry
> > > > > > > > > no
> > > > > > > > > > questions or
explanations (anyway Howard and other
> > maths
> > > > > people
> > > > > > > > > know
> > > > > > > > > > how to do that stuff).
> > > > > > > > > >
> > > > > > > > > >
> > > > > > > > > > --- In
amibroker@xxxxxxxxxps.com<amibroker%
40yahoogroups.com><amibroker%
> >
40yahoogroups.com><amibroker%
> >
> > > > >
40yahoogroups.com>,
> > > > > > > "brian_z111" <brian_z111@>
> > > > > > > > wrote:
> > > > > > > > > > >
> > > > > > > > > > > Gidday Mate,
> > > > > > > > > > >
> > > > > > > > > > > I wasn't
planning on posting again today as I am
> > going
> > > > > away
> > > > > > > for
> > > > > > > > a
> > > > > > > > > > few
> > > > > > > > > > > days ..... a
good question though so I couldn't
> > resist.
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > I did notice
Fred's comment on the priority he
> > places on
> > > > > > > > > > sensitivity
> > > > > > > > > > > analysis.
> > > > > > > > > > >
> > > > > > > > > > > He has made the
comment before and I came to
that
> > view
> > > > > > > > > > independently
> > > > > > > > > > > a way back
anyway (Howard's random noise test is
> > another
> > > > > > > > > > interesting
> > > > > > > > > > > idea for single
sample analysis).
> > > > > > > > > > >
> > > > > > > > > > > I also recall
that he doesn't believe
scrambling the
> > > > > order of
> > > > > > > > the
> > > > > > > > > > > trades provides
any meaningful feedback.
> > > > > > > > > > >
> > > > > > > > > > > That isn't a
reason for me not to reach my own
> > > > > conclusions.
> > > > > > > > > > >
> > > > > > > > > > > Fred has also
talked about small N retesting
(walk
> > > > > forward),
> > > > > > > > and
> > > > > > > > > > > adjusting his
system rules, on a short term
basis,
> > so
> > > > > while I
> > > > > > > > am
> > > > > > > > > > not
> > > > > > > > > > > keen on the idea
I am keeping an open mind on
the
> > > > subject.
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > > This is the
second time in the >past few
> > > > > > > > > > > > days that
you seem to have equated
> > trading/backtesting
> > > > > > > system
> > > > > > > > > > > >outcomes
> > > > > > > > > > > > to a random
series of coin flip outcomes
(random
> > > > binary
> > > > > > > > > > occurances).
> > > > > > > > > > > >
> > > > > > > > > > > > Serious
question... what is your point? What
is
> > the
> > > > > > > > relevence
> > > > > > > > > os
> > > > > > > > > > > >the
> > > > > > > > > > > > "Coin Flip"
metaphor where trading systems is
> > > > concerned?
> > > > > > > > > > >
> > > > > > > > > > > Well, developers
are selling software
specifically
> > > > > designed
> > > > > > > for
> > > > > > > > > > > performing MSC
for trading analysis and at
least one
> > > > guy
> > > > > has
> > > > > > > > > > written
> > > > > > > > > > > a book on the
subject.
> > > > > > > > > > >
> > > > > > > > > > > In both software
packages, that I have some
> > familiarity
> > > > > with,
> > > > > > > > > their
> > > > > > > > > > > model assumes
stationarity, and independency
i.e.
> > their
> > > > > model
> > > > > > > > > > treats
> > > > > > > > > > > the data as if
it is the outcome of a coin toss
with
> > > > > variable
> > > > > > > > > > values
> > > > > > > > > > > on the +- side
of the coin.
> > > > > > > > > > >
> > > > > > > > > > > This is a valid
model as long as stationarity
> > holds ...
> > > > I
> > > > > > > have
> > > > > > > > > > > simulated random
trading 'systems' and
predicted the
> > > > > outcome
> > > > > > > by
> > > > > > > > > > using
> > > > > > > > > > > binomial
probability, that references a
frequency
> > > > > > > distribution
> > > > > > > > of
> > > > > > > > > > the
> > > > > > > > > > > randomly
generated trades, and it predicted the
> > actual
> > > > > equity
> > > > > > > > > > > distributions
extremely well (a lognormal dist
> > appears
> > > > at
> > > > > > > very
> > > > > > > > > high
> > > > > > > > > > > N's).
> > > > > > > > > > >
> > > > > > > > > > > The value, to me
in that model, is that it is a
> > > > training
> > > > > tool
> > > > > > > > > that
> > > > > > > > > > > conditioned me
to accept variance as 'normal'
and
> > if the
> > > > > > > market
> > > > > > > > > is
> > > > > > > > > > > stationary then
it would have direct relevance
to
> > > > > > > trading.....
> > > > > > > > > the
> > > > > > > > > > > worst case
outcome would be that I could incur
> > losses,
> > > > > with a
> > > > > > > > > > > probability as
indicated by the Cumulative
> > Distrubution
> > > > > > > > Function
> > > > > > > > > > for
> > > > > > > > > > > the possible
equity outcomes (simulation is one
way
> > for
> > > > > non -
> > > > > > > > > > > mathematicians
to calc this and view it in a
chart).
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > Ask yourself ....
> > > > > > > > > > >
> > > > > > > > > > > afer you have
conducted a successful OOS, and
> > collated
> > > > the
> > > > > > > > trade
> > > > > > > > > > > sample, when you
start to trade it do you
expect:
> > > > > > > > > > >
> > > > > > > > > > > - all trades to
be the same, or similar, and
occur
> > with
> > > > > the
> > > > > > > > same
> > > > > > > > > > > frequency
(TradeSim),
> > > > > > > > > > > - all trades to
be the same, or similar, and
have
> > > > > variations
> > > > > > > in
> > > > > > > > > the
> > > > > > > > > > > frequency (MSA),
> > > > > > > > > > > - something else?
> > > > > > > > > > >
> > > > > > > > > > > Trading,
however, is not a coin toss.
> > > > > > > > > > >
> > > > > > > > > > > It is more like
a sample generator that produces
> > trades
> > > > > as a
> > > > > > > > > result
> > > > > > > > > > > of presenting
dynamic data to the system
(filter).
> > > > > > > > > > >
> > > > > > > > > > > To what extent
could a 'real life' trading
system
> > > > emulate
> > > > > a
> > > > > > > > coin
> > > > > > > > > > > toss, with
variable values ... how could that
come
> > > > about?
> > > > > > > > > > >
> > > > > > > > > > > (interesting
that the very functional optF
formula
> > came
> > > > > about
> > > > > > > > as
> > > > > > > > > > the
> > > > > > > > > > > variable value
coin toss staking formula).
> > > > > > > > > > >
> > > > > > > > > > > Is it possible
or not?
> > > > > > > > > > >
> > > > > > > > > > > A lot of people
seem to think it is, judging by
> > their
> > > > > books
> > > > > > > and
> > > > > > > > > > > software.
> > > > > > > > > > >
> > > > > > > > > > > Presumably, when
the underlying data changes,
the
> > sample
> > > > > > > > profile
> > > > > > > > > > > (mean, StDev
etc) can change and we end up with
a
> > > > better
> > > > > or
> > > > > > > > worse
> > > > > > > > > > > outcome than
anticipated by the OOS.
> > > > > > > > > > >
> > > > > > > > > > > So, does the
non-stationary behaviour of the
markets
> > > > > > > invalidate
> > > > > > > > > the
> > > > > > > > > > > coin toss model?
> > > > > > > > > > >
> > > > > > > > > > > That is the
ineresting question, and I don't
know
> > the
> > > > > answer
> > > > > > > to
> > > > > > > > > it,
> > > > > > > > > > > or even if there
is a definite answer.
> > > > > > > > > > >
> > > > > > > > > > > I was hopeful
that people would pick up on that
key
> > > > point
> > > > > and
> > > > > > > > > shed
> > > > > > > > > > > some light on
the subject.
> > > > > > > > > > >
> > > > > > > > > > > I know, from my
long hours of simulating random
> > data,
> > > > what
> > > > > > > > random
> > > > > > > > > > > behaviour looks
like when I see it.
> > > > > > > > > > >
> > > > > > > > > > > Clearly the
markets have a certain amount of
random
> > > > > behaviour.
> > > > > > > > > > >
> > > > > > > > > > > Howard commented
somewhere, or another, that
there
> > is a
> > > > > > > certain
> > > > > > > > > > > amount of
randomness in the market (I can't
recall
> > the
> > > > > method
> > > > > > > > he
> > > > > > > > > > used
> > > > > > > > > > > to measure it).
> > > > > > > > > > >
> > > > > > > > > > > It is quite easy
to observe if data has any
random
> > > > > qualities,
> > > > > > > > > > > especially if we
measure the core attributes
(50/50
> > > > heads
> > > > > and
> > > > > > > > > tails
> > > > > > > > > > > and its
persistence into 2,3,4 heads in a row
etc).
> > > > > > > > > > >
> > > > > > > > > > > Once again I ask
you to consider:
> > > > > > > > > > >
> > > > > > > > > > > if I measure the
S&P500 index, on close, and it
> > goes up
> > > > > > > approx
> > > > > > > > 50
> > > > > > > > > > and
> > > > > > > > > > > down approx 50
(+- variance that is typical of a
> > random
> > > > > > > > binomial
> > > > > > > > > > > event) and the
subsequent second head or tail
follow
> > > > with
> > > > > 0.5
> > > > > > > > > prob
> > > > > > > > > > > etc I am
justified in considering it top be a
pseudo
> > > > > random
> > > > > > > > > > binomail
> > > > > > > > > > > event?
> > > > > > > > > > >
> > > > > > > > > > > I have done
quick and dirty measurements, and
> > accurate
> > > > > > > > > > measurements,
> > > > > > > > > > > on dependency
(or on its inverse, which is
> > > > independency)
> > > > > and
> > > > > > > > find
> > > > > > > > > > > that there is a
good deal of independency in the
> > > > markets
> > > > > (I
> > > > > > > > > posted
> > > > > > > > > > > some q&d
code to measure that last week).
> > > > > > > > > > >
> > > > > > > > > > > I have
speculated before, on the point, that the
> > > > rational
> > > > > > > > market
> > > > > > > > > is
> > > > > > > > > > > the market that
follows fundamental value, which
> > tends
> > > > to
> > > > > be
> > > > > > > >=
> > > > > > > > > the
> > > > > > > > > > > yearly (macro)
timeframe, and, everything else
is
> > the
> > > > > > > > irrational
> > > > > > > > > > > market.
> > > > > > > > > > >
> > > > > > > > > > > Consider an
intraday market ... what is rational
> > about
> > > > the
> > > > > > > > price
> > > > > > > > > > > movement during
any given part of the day?
> > > > > > > > > > >
> > > > > > > > > > > - Draw a trend
line on the chart .. we will
assume
> > that
> > > > we
> > > > > > > know
> > > > > > > > > > what
> > > > > > > > > > > a trend is for
this exercise, although that is a
> > > > debatable
> > > > > > > > point.
> > > > > > > > > > >
> > > > > > > > > > > - The trend, a
straight line, is rational (it is
> > > > perfectly
> > > > > > > > > > following
> > > > > > > > > > > fundamental
value).... it is 2007 and it is
up ;-)
> > > > > > > > > > >
> > > > > > > > > > > - All of the ups
and downs that occur around it
are
> > > > > > > irrational
> > > > > > > > > > > (bucking the
trend).
> > > > > > > > > > >
> > > > > > > > > > > - The trend line
goes under the pivot lows.
> > > > > > > > > > >
> > > > > > > > > > > - Your system
buys at the pivot lows and sells
at =
> > = 2
> > > > > StDev
> > > > > > > > > above
> > > > > > > > > > > the trend line.
> > > > > > > > > > >
> > > > > > > > > > > - Place a stop
under the trend line at - 1
stDev.
> > > > > > > > > > >
> > > > > > > > > > > - Assume no
commission and no slippage.
> > > > > > > > > > >
> > > > > > > > > > > - Your payoff
ratio is 2/1
> > > > > > > > > > >
> > > > > > > > > > > - assume there
is no variance in volatility so
the
> > PR
> > > > is a
> > > > > > > > > constant
> > > > > > > > > > > value
> > > > > > > > > > >
> > > > > > > > > > > - the win/loss
ratio is determined by the random
> > > > > meandering
> > > > > > > of
> > > > > > > > > the
> > > > > > > > > > > irrational price
movements up and down.
> > > > > > > > > > >
> > > > > > > > > > > Note they are
irrational because people are
buying
> > and
> > > > > > > selling
> > > > > > > > at
> > > > > > > > > > the
> > > > > > > > > > > wrong time and
for the wrong reasons - if they
were
> > > > > rational
> > > > > > > > they
> > > > > > > > > > > would only be
buying selling as fundamental
values
> > > > change.
> > > > > > > > > > >
> > > > > > > > > > > - the trade
series produced would look exactly
that
> > that
> > > > > > > > produced
> > > > > > > > > > by
> > > > > > > > > > > a coin tossed
with +2, -1 value on it.
> > > > > > > > > > >
> > > > > > > > > > > Now, you have
tested this system, OOS, and it
is a
> > > > winner.
> > > > > > > > > > >
> > > > > > > > > > > What chance for
stationarity when you trade
live?
> > > > > > > > > > >
> > > > > > > > > > > If the trend
continues there is a very good
chance
> > that
> > > > > the
> > > > > > > > > random
> > > > > > > > > > > emualator
(system meeting dynamic data) will
> > continue to
> > > > > > > > perform
> > > > > > > > > > like
> > > > > > > > > > > a biased coin +-
variance i.e. the payoff ratio
> > can't
> > > > > change
> > > > > > > > but
> > > > > > > > > > the
> > > > > > > > > > > W/L will (it
always does when I toss a coin).
> > > > > > > > > > >
> > > > > > > > > > > If the trend
changes your winning model will be
more
> > > > > likely
> > > > > > > to
> > > > > > > > > bust.
> > > > > > > > > > >
> > > > > > > > > > > That could be
the reason Fred, and others, like
to
> > > > > > > continually
> > > > > > > > > > retest.
> > > > > > > > > > >
> > > > > > > > > > > I have another
approach to getting around this
> > problem
> > > > > (this
> > > > > > > is
> > > > > > > > > > > actually the
real point of my posts) ...
> > > > > > > > > > >
> > > > > > > > > > > ..... to
accomodate non-stationarity either
adjust
> > > > > quickly OR
> > > > > > > > use
> > > > > > > > > a
> > > > > > > > > > > dimensionless
model e.g. don't believe in
trends and
> > > > then
> > > > > you
> > > > > > > > > can't
> > > > > > > > > > > be on the wrong
side of them.
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > However, that is
only speculation.
> > > > > > > > > > >
> > > > > > > > > > > What do you
think?
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > Again ... what
is the relevance of coin tosses
to
> > > > trading
> > > > > IMO:
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > - wonderful
training tool
> > > > > > > > > > > - a good OOS can
not predict exactly what the
> > outcome
> > > > of
> > > > > live
> > > > > > > > > > trading
> > > > > > > > > > > will be (subject
to nonstationarity) and
neither can
> > > > > > > simulation
> > > > > > > > > > (coin
> > > > > > > > > > > tossing) but it
gives a good approximation of
the
> > > > > > > possibilities
> > > > > > > > > > (also
> > > > > > > > > > > subject to
non-stationarity)
.
> > > > > > > > > > >
> > > > > > > > > > > As a quid pro
quo .....
> > > > > > > > > > >
> > > > > > > > > > > ..... if you, or
anyone else, can give me any
> > > > explanation
> > > > > > > > and/or
> > > > > > > > > > > proof that the
coin toss metaphor has no
relevance
> > to
> > > > > trading
> > > > > > > I
> > > > > > > > > > would
> > > > > > > > > > > be delighted.
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > Anyway, I think
Patrick already answered the
> > question,
> > > > or
> > > > > > > told
> > > > > > > > us
> > > > > > > > > > > where to find it.
> > > > > > > > > > >
> > > > > > > > > > > Good luck with
your trading.
> > > > > > > > > > >
> > > > > > > > > > >
brian_zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
> > > > > > > > > > >
> > > > > > > > > > >
> > > > > > > > > > > --- In amibroker@xxxxxxxxxps.com<amibroker%
40yahoogroups.com>
> > <amibroker%
> > 40yahoogroups.com><amibroker%
> >
> > > > > 40yahoogroups.com>,
> > > > > > > "Phsst" <phsst@> wrote:
> > > > > > > > > > > >
> > > > > > > > > > > > Hello Brian,
> > > > > > > > > > > >
> > > > > > > > > > > > Thanks for
the mention in your New Years
post. I
> > felt
> > > > > > > > humbled
> > > > > > > > > to
> > > > > > > > > > > be in
> > > > > > > > > > > > the same
honerable mention list as Fred (He
is a
> > very
> > > > > smart
> > > > > > > > > Dude
> > > > > > > > > > (no
> > > > > > > > > > > > kidding!))
It took me a while (some years
back) to
> > > > > figure
> > > > > > > out
> > > > > > > > > > what a
> > > > > > > > > > > > smart guy
Fred really is. I've since learned
that
> > > > when
> > > > > Fred
> > > > > > > > > > speaks,
> > > > > > > > > > > it
> > > > > > > > > > > > pays to
think and be silent for a good long
while
> > > > before
> > > > > > > > > drawing
> > > > > > > > > > any
> > > > > > > > > > > > conclusions.
> > > > > > > > > > > >
> > > > > > > > > > > > To your
"crystal clear" point... This is the
> > second
> > > > > time in
> > > > > > > > the
> > > > > > > > > > > past few
> > > > > > > > > > > > days that
you seem to have equated
> > trading/backtesting
> > > > > > > system
> > > > > > > > > > > outcomes
> > > > > > > > > > > > to a random
series of coin flip outcomes
(random
> > > > binary
> > > > > > > > > > occurances).
> > > > > > > > > > > >
> > > > > > > > > > > > Serious
question... what is your point? What
is
> > the
> > > > > > > > relevence
> > > > > > > > > os
> > > > > > > > > > > the
> > > > > > > > > > > > "Coin Flip"
metaphor where trading systems is
> > > > concerned?
> > > > > > > > What
> > > > > > > > > am
> > > > > > > > > > I
> > > > > > > > > > > > missing?
> > > > > > > > > > > >
> > > > > > > > > > > > Your Bud...
Phsst
> > > > > > > > > > > >
> > > > > > > > > > > >
> > > > > > > > > > > >
> > > > > > > > > > > > This is the
second time
> > > > > > > > > > > > --- In amibroker@xxxxxxxxxps.com<amibroker%
40yahoogroups.com>
> > <amibroker%
> > 40yahoogroups.com><amibroker%
> >
> > > > > 40yahoogroups.com>,
> > > > > > > "brian_z111"
> > > > > > > <brian_z111@>
> > > > > > > > > > wrote:
> > > > > > > > > > > > >
> > > > > > > > > > > > > To be
chrystal clear about my hypothesis:
> > > > > > > > > > > > >
> > > > > > > > > > > > >
> > > > > > > > > > > > > We are
trying to design a system that
produces
> > the
> > > > > same
> > > > > > > set
> > > > > > > > of
> > > > > > > > > > > > >
trades, in the future, as it has in the
past i.e
> > > > > trades
> > > > > > > and
> > > > > > > > > not
> > > > > > > > > > > > >
combinations of trades.
> > > > > > > > > > > > >
> > > > > > > > > > > > > If a
solid gold coin, minted by the US
treasury,
> > > > with
> > > > > a
> > > > > > > > head
> > > > > > > > > > and a
> > > > > > > > > > > > > tail
clearly stamped on each side, and only
two
> > > > > values +1
> > > > > > > > or -
> > > > > > > > > 1
> > > > > > > > > > > can't
> > > > > > > > > > > > >
reproduce two equity curves that look the
same,
> > > > after
> > > > > N
> > > > > > > > > tosses,
> > > > > > > > > > > how
> > > > > > > > > > > > > can we
expect a trading system to do that
when
> > it
> > > > has
> > > > > a
> > > > > > > > range
> > > > > > > > > of
> > > > > > > > > > > > >
possible values?
> > > > > > > > > > > > >
> > > > > > > > > > > > > AND it
doesn't get any better as N
increases.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Put
your time and effort into maximising the
> > > > STABILITY
> > > > > > > > > > > > >
(predictability, boundness) of the trade
> > set 'with
> > > > an
> > > > > > > edge'
> > > > > > > > > > THEN
> > > > > > > > > > > use
> > > > > > > > > > > > > MM to
optimise the equity outcome the system
> > > > produces
> > > > > > > > > (optimise
> > > > > > > > > > ==
> > > > > > > > > > > > > your
definition e.g. max return, min risk or
> > > > > whatever).
> > > > > > > > > > > > >
> > > > > > > > > > > > >
> > > > > > > > > > > > >
> > > > > > > > > > > > >
> > > > > > > > > > > > > --- In
amibroker@xxxxxxxxxps.com<amibroker%
40yahoogroups.com>
> > <amibroker%
> > 40yahoogroups.com><amibroker%
> >
> > > > > 40yahoogroups.com>,
> > > > > > > "brian_z111"
> > > > > > > brian_z111@
> > > > > > > > > > wrote:
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Howard,
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Thanks for your post.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > A
very well written article.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Some contrary comment (first referencing
some
> > of
> > > > > your
> > > > > > > > > points
> > > > > > > > > > and
> > > > > > > > > > > > > >
then, later, some comments of my own):
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> By trying many
> > > > > > > > > > > > > >
> combinations of logic and parameter
values,
> > we
> > > > > will
> > > > > > > > > > eventually
> > > > > > > > > > > > > find
> > > > > > > > > > > > > >
>a system that is profitable for the date
> > range
> > > > > > > analyzed.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
You are assuming that all successful long
term
> > > > > traders
> > > > > > > > > > arrived
> > > > > > > > > > > at
> > > > > > > > > > > > > >
their system(s) by using this approach ...
> > perhaps
> > > > > > > there
> > > > > > > > > are
> > > > > > > > > > > > > systems
> > > > > > > > > > > > > >
out there that have no optimiseable
parameters
> > > > and
> > > > > only
> > > > > > > > one
> > > > > > > > > > > > > >
underlying logic.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
If so they are likely be based on primal
> > market
> > > > > > > behaviour
> > > > > > > > > and
> > > > > > > > > > > > > >
therefore persistent across markets and
time
> > i.e
> > > > > they
> > > > > > > > would
> > > > > > > > > > > have to
> > > > > > > > > > > > > >
be systems based on market characteristics
> > that
> > > > are
> > > > > > > > > relatively
> > > > > > > > > > > > > >
stationary.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> testing the
> > > > > > > > > > > > > >
> profitability of a trading system that
was
> > > > > developed
> > > > > > > > > using
> > > > > > > > > > > recent
> > > > > > > > > > > > > >
>data
> > > > > > > > > > > > > >
> on older data is guaranteed to over-
> > estimate the
> > > > > > > > > > > profitability of
> > > > > > > > > > > > > >
the
> > > > > > > > > > > > > >
> trading system.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
You know that in science
(philosophy/logic) it
> > > > only
> > > > > > > takes
> > > > > > > > > one
> > > > > > > > > > > > > >
refutation to dethrone the current ruling
> > > > > hypothesis ...
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
if a long system, developed on the last 12
> > months
> > > > of
> > > > > > > data
> > > > > > > > > > (when
> > > > > > > > > > > the
> > > > > > > > > > > > > >
market was experiencing a bear riot) is
then
> > > > tested
> > > > > OOS
> > > > > > > > on
> > > > > > > > > the
> > > > > > > > > > > > > prior
> > > > > > > > > > > > > >
years data it will outperform the in
sample
> > tests
> > > > > (OOS
> > > > > > > > > would
> > > > > > > > > > be
> > > > > > > > > > > > > >
conducted on bull market data).
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> There is very little reason to expect
that
> > > > future
> > > > > > > > > behavior
> > > > > > > > > > and
> > > > > > > > > > > > > >
> profitability of well known trading
systems
> > > > will
> > > > > be
> > > > > > > the
> > > > > > > > > > same
> > > > > > > > > > > as
> > > > > > > > > > > > > past
> > > > > > > > > > > > > >
> behavior.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Do we have any empirical evidence of this?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
First we would have to have an agreed
> > definition
> > > > > > > of 'well
> > > > > > > > > > > known',
> > > > > > > > > > > > > >
make a list of the systems, and then
perform
> > > > massive
> > > > > > > > > testing.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
To scrupulously prevent any bias creeping
> > testing
> > > > > would
> > > > > > > > > have
> > > > > > > > > > to
> > > > > > > > > > > be
> > > > > > > > > > > > > >
conducted live, and not on historical
data.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
We only know that they were
successful 'in the
> > > > > past' by
> > > > > > > > IS
> > > > > > > > > > > testing,
> > > > > > > > > > > > > >
or by claim.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Do we have any, or many, certified
performance
> > > > > records
> > > > > > > > > > provided
> > > > > > > > > > > by
> > > > > > > > > > > > > >
traders who claim to have had success with
> > > > > those 'well
> > > > > > > > > known'
> > > > > > > > > > > > >
systems.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> Statistics gathered from in-sample
results
> > have
> > > > > > > > > > > > > >
> no relationship to statistics that will
be
> > > > > gathered
> > > > > > > > from
> > > > > > > > > > > trading.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Not, so.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
They have every bearing on the stats
gathered
> > in
> > > > > > > trading
> > > > > > > > > > because
> > > > > > > > > > > > > only
> > > > > > > > > > > > > >
systems with good IS performance make it
to
> > the
> > > > OS,
> > > > > or
> > > > > > > > live
> > > > > > > > > > > > >
trading,
> > > > > > > > > > > > > >
phase.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
OOS testing is only proceeded with
because the
> > > > > analyst
> > > > > > > > has
> > > > > > > > > > every
> > > > > > > > > > > > > >
expectation, or hope, that the good IS
stats
> > will
> > > > be
> > > > > > > > > > reproduced
> > > > > > > > > > > OOS.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
In fact it is the relative performance
between
> > > > the
> > > > > IS
> > > > > > > and
> > > > > > > > > OOS
> > > > > > > > > > > stats
> > > > > > > > > > > > > >
the encourages us to proceed or abort.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Re trading the edge erodes the edge:
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
It is an assumption that all players are
> > trading
> > > > > > > > > systems ...
> > > > > > > > > > > many
> > > > > > > > > > > > > are
> > > > > > > > > > > > > >
not, in fact the vast majority are not....
> > those
> > > > who
> > > > > > > > aren't
> > > > > > > > > > > control
> > > > > > > > > > > > > >
vastly greater sums of money than those
who
> > do.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
It is an assumption that all wins erode
the
> > > > > system ...
> > > > > > > > they
> > > > > > > > > > > could
> > > > > > > > > > > > > be
> > > > > > > > > > > > > >
just lucky wins that the trader can't
exploit
> > long
> > > > > > > term,
> > > > > > > > or
> > > > > > > > > > > > > >
successful wins that the trader doesn't
> > sustain
> > > > e.g
> > > > > > > they
> > > > > > > > > > might
> > > > > > > > > > > not
> > > > > > > > > > > > > >
have the capital, use the correct staking
or
> > > > > maintain
> > > > > > > > self-
> > > > > > > > > > > > >
discipline
> > > > > > > > > > > > > >
in the future.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Only a very small percentage of traders
are
> > > > > successful,
> > > > > > > > and
> > > > > > > > > > > hence
> > > > > > > > > > > > > >
trading a successful system ... every one
else
> > > > who
> > > > > is
> > > > > > > > > trading
> > > > > > > > > > is
> > > > > > > > > > > > > just
> > > > > > > > > > > > > >
making noise.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
There are millions of system permutations,
> > > > > instruments,
> > > > > > > > > > markets,
> > > > > > > > > > > > > >
staking systems etc ..... how many
successful
> > > > > traders
> > > > > > > > would
> > > > > > > > > > it
> > > > > > > > > > > take
> > > > > > > > > > > > > >
to exahaust all of the successful
> > permutations?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> The follow-on point, which relates to
Monte
> > > > Carlo
> > > > > > > > > analysis,
> > > > > > > > > > is
> > > > > > > > > > > > > that
> > > > > > > > > > > > > >
> rearranging the in-sample trades gives
no
> > > > insight
> > > > > > > into
> > > > > > > > > the
> > > > > > > > > > > future
> > > > > > > > > > > > > >
> characteristics of the system. Yes, you
can
> > see
> > > > > the
> > > > > > > > > effect
> > > > > > > > > > of
> > > > > > > > > > > > > taking
> > > > > > > > > > > > > >
> the trades in different orders. But why
> > bother?
> > > > > They
> > > > > > > > are
> > > > > > > > > > still
> > > > > > > > > > > > > >
> in-sample results and still have no
value.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
If you are engineering an F1 racing car
there
> > is
> > > > > only
> > > > > > > > track
> > > > > > > > > > > > > >
testing/simulation (99.9 of the time) and
> > racing
> > > > > > > > > performance
> > > > > > > > > > > (1% of
> > > > > > > > > > > > > >
the time).
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
The more information you gather off the
track
> > the
> > > > > more
> > > > > > > > > likely
> > > > > > > > > > > you
> > > > > > > > > > > > > are
> > > > > > > > > > > > > >
to perform on the track OR know what to
adjust
> > > > and
> > > > > when
> > > > > > > > to
> > > > > > > > > > > adjust
> > > > > > > > > > > > > it
> > > > > > > > > > > > > >
if performance doesn't meet expectations.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Do you know of any F1 teams that don't
> > > > > test/simulate?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Do you know of any F1 teams that only
> > > > test/simulate
> > > > > > > one,
> > > > > > > > or
> > > > > > > > > > > > >
limited,
> > > > > > > > > > > > > >
metrics?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
What is testing if not 'massive
examination of
> > > > what-
> > > > > if
> > > > > > > > > > > scenarios'?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Re MonteCarlo and stationarity
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I
haven't studied the subject in depth.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Mainly it is has been used outside of
trading
> > and
> > > > in
> > > > > > > > > > different
> > > > > > > > > > > ways
> > > > > > > > > > > > > >
to the ways that traders use it ....
possibly
> > it
> > > > > would
> > > > > > > > be
> > > > > > > > > > best
> > > > > > > > > > > to
> > > > > > > > > > > > > >
limit trading discussion to 'trading
> > simulation'
> > > > and
> > > > > > > drop
> > > > > > > > > the
> > > > > > > > > > MC
> > > > > > > > > > > > > part
> > > > > > > > > > > > > >
of the name.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I
have only found one book devoted to the
> > subject
> > > > > and I
> > > > > > > > > regret
> > > > > > > > > > > > > buying
> > > > > > > > > > > > > >
it .... 'MCS and System Trading' by Volker
> > > > Butzlaff.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I
have also test driven TradeSim and MSA.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Referencing their trading apps.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
TS arranges the trades, as a time series,
and
> > > > > randomly
> > > > > > > > > walks
> > > > > > > > > > > > > through
> > > > > > > > > > > > > >
all permutations to simulate 'live
> > trading'.....
> > > > it
> > > > > is
> > > > > > > an
> > > > > > > > > MM
> > > > > > > > > > > test,
> > > > > > > > > > > > > of
> > > > > > > > > > > > > >
some kind, because equity is allocated
prior
> > to
> > > > the
> > > > > > > walk
> > > > > > > > > > > through.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
AB's backtester, in default mode, does
this
> > once.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I
assume other methods could be used ...
as
> > per my
> > > > > > > > pervious
> > > > > > > > > > XYZ
> > > > > > > > > > > > > >
example:
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > -
abcXdefghi with simultaneous trades on
day
> > 4,
> > > > > > > > > > > > > > -
we can only achieve a finite set of
> > > > permutations,
> > > > > > > > > > > > > > -
the outcome of massive sampling will
tend to
> > > > the
> > > > > mean
> > > > > > > +-
> > > > > > > >
> > > > > > > > > > > variance,
> > > > > > > > > > > > > > -
we can simulate the eq outcomes using
random
> > > > > sampling
> > > > > > > > of
> > > > > > > > > > > uniform
> > > > > > > > > > > > > >
size, ave the result per random series and
> > then
> > > > freq
> > > > > > > dist
> > > > > > > > > the
> > > > > > > > > > > means
> > > > > > > > > > > > > >
(Central Limit Theoreom predicts a pseudo
norm
> > > > > dist).
> > > > > > > > > > > > > >
> 30 selections per series * ? series will
> > > > achieve
> > > > > an
> > > > > > > > > approx
> > > > > > > > > > of
> > > > > > > > > > > > > >
possible eq outcomes (I'm not sure if
> > > > distrubtions
> > > > > obey
> > > > > > > > the
> > > > > > > > > > > laws of
> > > > > > > > > > > > > >
sample error ... I don't think they do).
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
TradeSims real life simulation assumes
> > > > stationarity
> > > > > > > (the
> > > > > > > > > > balls
> > > > > > > > > > > in
> > > > > > > > > > > > > the
> > > > > > > > > > > > > >
bin, and their values will remain constant
> > into
> > > > the
> > > > > > > > future).
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
It also assumes that they will be selected
> > from
> > > > the
> > > > > bin
> > > > > > > > in
> > > > > > > > > > the
> > > > > > > > > > > same
> > > > > > > > > > > > > >
order, or frequency to be absolutely
correct
> > (the
> > > > > order
> > > > > > > > > > doesn't
> > > > > > > > > > > > > >
change anything only the frequency)....
to be
> > > > > precise
> > > > > > > > about
> > > > > > > > > > it,
> > > > > > > > > > > > > their
> > > > > > > > > > > > > >
model assumes that if you have picked the
> > worst
> > > > > > > > historical
> > > > > > > > > > loss
> > > > > > > > > > > out
> > > > > > > > > > > > > >
of the bin 2/1000 trades that you will not
> > only
> > > > > > > > experience
> > > > > > > > > > the
> > > > > > > > > > > same
> > > > > > > > > > > > > %
> > > > > > > > > > > > > >
as the worst loss in the future but that
it
> > will
> > > > > also
> > > > > > > > only
> > > > > > > > > > occur
> > > > > > > > > > > > > >
2/1000 times.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
MSA puts all of the balls in the bin and
> > selects
> > > > > them
> > > > > > > in
> > > > > > > > a
> > > > > > > > > > way
> > > > > > > > > > > that
> > > > > > > > > > > > > >
allows new combinations (frequencies)
until
> > all
> > > > > possible
> > > > > > > > > > > > >
frequencies
> > > > > > > > > > > > > >
are exhausted i.e. they assume
stationarity
> > only
> > > > in
> > > > > > > > values
> > > > > > > > > > but
> > > > > > > > > > > not
> > > > > > > > > > > > > >
frequency of dist (they assume dist is a
> > > > probability
> > > > > > > > > > statement
> > > > > > > > > > > and
> > > > > > > > > > > > > >
not a constant or series of
constants).... to
> > be
> > > > > > > precise
> > > > > > > > > > about
> > > > > > > > > > > it
> > > > > > > > > > > > > >
they assume that if it can happen it will.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
So, stationarity is the issue.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
So many people are confusing variance with
> > non-
> > > > > > > > > > stationarity ....
> > > > > > > > > > > > > they
> > > > > > > > > > > > > >
are being fooled by randomness e.g.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
we know that the trial records of fair
coin
> > > > tosses
> > > > > are
> > > > > > > > > > > stationary
> > > > > > > > > > > > > AND
> > > > > > > > > > > > > >
they have a surprising range of outcomes
> > > > > (variance) ...
> > > > > > > > > this
> > > > > > > > > > is
> > > > > > > > > > > > > very
> > > > > > > > > > > > > >
easy to see if simulated and expressed as
> > equity
> > > > > > > outcomes.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Therefore, in trading, we can, at the
least
> > > > expect a
> > > > > > > > > > tremendous
> > > > > > > > > > > > > >
amount of variance ... no less than what
can
> > be
> > > > > > > expected
> > > > > > > > > from
> > > > > > > > > > a
> > > > > > > > > > > > > coin
> > > > > > > > > > > > > >
toss experiment ... this variance can be
> > estimated
> > > > > > > using
> > > > > > > > > > several
> > > > > > > > > > > > > >
methods, simulation being one easy, push
the
> > > > > computer
> > > > > > > > > button
> > > > > > > > > > and
> > > > > > > > > > > > > look
> > > > > > > > > > > > > >
at the graph method.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
So, the value of the simulation is in
training
> > > > the
> > > > > mind
> > > > > > > > to
> > > > > > > > > > > accept
> > > > > > > > > > > > > >
variance and mentally prepare for the
worst
> > case
> > > > > losses.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
However, it doesn't matter how we design
our
> > > > > systems we
> > > > > > > > can
> > > > > > > > > > not
> > > > > > > > > > > do
> > > > > > > > > > > > > >
anything about stopping non-stationarity.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
Our system will get wiped out in OOS if
it is
> > not
> > > > > > > robust
> > > > > > > > OR
> > > > > > > > > > if
> > > > > > > > > > > the
> > > > > > > > > > > > > >
market changes.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
If our system is robust it will still get
> > wiped
> > > > out
> > > > > if
> > > > > > > > the
> > > > > > > > > > > market
> > > > > > > > > > > > > >
changes.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
However, IMO, non-stationarity is not, or
need
> > > > not
> > > > > be,
> > > > > > > as
> > > > > > > > > > > pervasive
> > > > > > > > > > > > > >
in trading as we think.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > >
As I have said in the past, and already in
> > this
> > > > > > > post ...
> > > > > > > > > many
> > > > > > > > > > > > > traders
> > > > > > > > > > > > > >
are slayed by the innocuous looking Black
> > Swan,
> > > > > because
>