|
PureBytes Links
Trading Reference Links
|
Here is a discussion from another email list on adaptive systems.
adaptive systems is pretty
complicated matter.
there are several known ways
of doing it, at least about 4.
the math is not too complicated but
arcane and the concept is
hard to comprehend.
there are several questions:
what does adaptive system mean?
what do you adapt it to?
what to adapt?
what do you adapt it based on?
how do you do it?
what is the math?
how to you implement it in code?
is it doable?
adaptive means the system's algorithm
tunes itself up as the "market footprint"
changes to maximize the performance
criterion which is max reward at min risk.
if you want to discuss adaptive first you
have to discuss non adaptive systems
like the ones you can code in TSs.
the main objective of any system is to
find the balance in between the risk
and the reward - which is the main
criteria. in TS we do that by running
optimization and finding the suitable
peak in the optimization function.
optimization function (OF) has a
dependent and independent variables.
dependent variables are Max Profit (MP)
and Min Risk (MR), independent are
your parameters / inputs ( I )
example: if you have 3 inputs 3 Is
your OF will is 4 or 5 dimensional
( 3 Is + MR + MP ). this could be
graphically representing as a multidimensional
surface. the key is to find the peak of
that surface( that's why if system has more
than 3 inputs i toss it ) - hard to do
because it's hard to visualize.
you can see now that if a system does not
adapt you have to find the peak manually
or you have to compromise.
*most systems fail because they are not
adaptive - curvefitted!!!
so, the purpose of adaptive system is
to find that peak in OF in real time.
to know the peak you need to know
the OF. to know OF you have to
know: MR, MP, and all Is.
let's break it down.
MR and MP: you have to calculate
systems performance in real time.
but the system does not know how
it performs itself. it needs some criteria
to go by. how can a system know
if it works on all cylinders and bangs
out max profit at min reward or just
barely making it? you have to give it
a reference to go by. this ref performance
is called system efficiency (SE). SE is
calculated in % by comparing in real time
the performance of real system to
the performance of ideal system. another
term needs to be introduced - ideal system.
ideal system buys the very top and sells
the very bottom. you can easily calculate
that buy coding a function that will sell
and buy in hindsight and give you
max possible profit at zero risk.
now, then you take ideal system as 100%
efficiency, then your
SE = real performance / ideal performance.
say your average SE = 30% that means
you are pulling out 30% or what you can pull
out of the market. this becomes the criterion
to go by in adaptation or Max SE.
this can fluctuate from Min allowable SE
say 20% to 100% ( will never be 100%).
based on statistical runs you can then calculate
mean SE to go by, say 30%.
now you know what to adapt to.
next is what to adapt:
well, obviously you have to adapt your
parameters or inputs - your Is.
you have to tune your inputs to get the highest
SE. that's where it gets real tricky.
to be able to do that you need OF- you need that
curve to tell you what the parameters should
be to get max SE. let's leave this out for a second.
next is what do you adapt based on:
you adapt based on changing market conditions
or what i call changing "market footprint".
every instrument traded out there has it's own
particular market footprint which is:
a compilation of statistical variables common
to all instruments, like: ave true range ( bar velocity),
ave volatility, volatility std, average volume,
liquidity and so on. footprint is a set of
statistical parameters that you can use as fingerprints
to identify and differentiate between different
instruments you trade. this footprint will change
in real time... volatility will fluctuate, so will volume,
average bar range, etc. one day SP can trade
real narrow range with low volume, the next day
volatility can explode - market footprint changed.
next is how to adapt it.
well, the first thing that should pop into your mind
is that you need a feedback loop of some sort.
the rational loop is this:
footprint changed -> adjust parameters ->
to maximize SE ratio -> if SE drops means
footprint changed -> repeat.
if you examine this loop you'll notice that
you need at least 2 functions ( transfer functions )
to do that:
1. parameters = f ( footprint )
2. SE = f( parameters )
of you can rewrite it as:
SE = f ( f ( footprint ) ); tells you systems
efficiency will fluctuate based on changing
market conditions.
so where do you get those functions:
a. from a sample run: you do a pass
over data, build your OF function and
then build your parameter = f( footprint )
function. log it in and use it for the real
time run. you can keep updating those
functions in real time. this is similar to
manual optimization where you do
sample runs but in addition to that
the OF gets updated in real time.
b. ramp up period. you start with
a ramp up period and update your
1 and 2 functions as you go along
your SE will start with 0% and will be
improving as those functions
will be more and more accurate.
the system like this will start trading
real bad and then improve it's performance
as it adapts and learns to trade better and better.
the performance will taper off and stabilize
as those functions are saturated.
c. multiple parallel models: you run
multiple systems based on different
parameters and find the best performing
one under changing market footprint and trade
that best one.
this approach however does not guarantee
that the best performing current model
will continue to be the best tomorrow.
John Clayburg implemented this approach
by running parallel performance functions
in TS. it showed a little bit of improvement
but not much. the reason again that
you are chasing the best performing model
that will not necessarily continue to perform
good tomorrow ( best fit today is not
necessarily will be the best fit tomorrow )
d. my approach. since i already went through all
of the bs in paragraphs a through c what i do
is the direct analytical approach - a shortcut.
i ask myself a question - how
this specific market variable will affect
my SE ( systems efficiency, performance ) or my
P&L through direct math. first i try to tie as many
parameters to market footprint ( market variable )
it allows me to make a shortcut and i don't have
to find parameter = f ( market footprint ) function.
market footprint becomes the parameter itself.
next, i try to answer the question of how will
this market variable affect my PL analytically -
i try to find SE = f ( footprint ) function by
studying how, say, volatility affects my PL in
the signal generator. if market becomes noisy
how will it affect my PL in the system.
the answer is simple: more noise you got
less money you make.
last step is to measure market variable ( market
footprint ) and through those functions adjust
your algorithm to pump up your SE.
this is the right approach and the best one.
in short, your adaptive techniques should be
built right into your trading algorithm.
- define market footprint ( which market variables hurt or
improve your systems performance ) then
- use those as your parameters so that the market will
itself adjust those for you then
- define your signal generating algorithm to include
those parameters and specify how those will
affect your systems performance.
-specify how your trading algorithm should change
based on that parameter.
that's it. it becomes self adaptive.
an example:
market footprint = noise level
noise level = your parameter
more noise -> less profit
less noise -> more profit.
if more noise then increase risk and lengthen
time horizon to maximize profit and minimize
loss.
if less noise then decrease risk and
shorten time horizon to maximize profit and minimize
loss.
a common parameter is lookback. in MA.
well, going by what is said is MA lookback has anything
to do with a market footprint market variable - nope.
you can't differentiate markets by MA lookback - toss it.
another common lookback variable - ATR ( lookback ) -defines
a lookback in average true range calculation.
can ATR be used as a market variable to define market
footprint? possibly can. that's why ATR often referred
to as "adaptive" variable - changing. but even
ATR can vary based on lookback used. so, it's semi
adaptive, you still have the lookback to deal with.
it is self evident that the first step in designing adaptive
systems is to define market footprint
in variables that require no parameters or
or allow only parameters will not affect
variable measurement itself.
if you try to define noise through ATR then
ATR is dependent on lookback unless the lookback
value is high. but then if lookback value is high, ATR
will not be sensitive to it's most recent change. :-)
go figure.
volatility also requires lookback.
almost everything there needs a damn lookback or a factor.
however if you isolate the most recent swing ( current trade )
in the price and find pivot high and pivot low and find
the duration of that swing and use that duration as a lookback
then what your saying is that i only want to measure noise
during the most current trade that i am in... this becomes
adaptive lookback and ATR becomes adaptive.
then your market variable can be called - ATR of last tradable
swing... and not ATR of some arbitrary lookback that
you think is suitable.
at the end it all comes down to about 4-5 market variables
that you need to define and most of them have to do with
volatility in one form of the other. volatility is the main market
variable!
- untradable volatility = noise = risk = lag
- min tradable volatility = vector deviation = min signal = reward = profit
or loss differential.
- max tradable volatility = vector volatility = max signal = trend = sum of
all positive and negative
profit differentials ( profitable and unprofitable trades - risk and
reward )= your total P&L.
find noise then you can find the signal,
find the signal then you can find the trend.
find the trend then you are done.
just don't use any fixed lookbacks and factors :-)
this is pretty much it without any hard math thrown in.
bilo.
ps. markets are dynamic, most systems are static
that's why most systems don't work.
and if you add irrational buy and sell rules on top of many
input parameters, they don't work at all.
----- Original Message -----
From: "rudolf stricker" <lists@xxxxxxxxxxx>
To: <metastock@xxxxxxxxxxxxx>
Sent: Wednesday, February 06, 2002 12:16 PM
Subject: adaptive systems - how to define appropriate time windows ?
>
> List,
>
> using an adaptive system for day-to-day trading of DAX options, I
> wonder, which criteria might be helpful to define "the best" time
> window to deal with ... Presently, I use a 5 years window, where the
> rating criteria to select an appropriate system are weighted something
> like exponentially over time.
>
> But at these rapidly changing markets, I get some unsatisfactory
> results: While my system shows nice results e.g. for long puts over
> the last year or so, this potential couldn't be used: my money
> management (based on 5 years) nearly stops me out from trading these
> system results, because the strategy working well for the last year
> doesn't show good results for at least some of the years before.
>
> So my questions are:
>
> What time period may be appropriate to construct a(n adaptive) trading
> system for a given equity?
> What criterions (to read from the equity's historical data) could help
> to define "the best" time period?
> What other aspects may be important to define an appropriate time
> window?
>
> Any hint is welcome ...
>
> mfg rudolf stricker
> | Disclaimer: The views of this user are strictly his own.
>
>
|