Requisite Variety
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Exogenous_Data_Based_Models.htm
train your quants to protect your portfolio against the ill effects of
nonstationarity. Quantitative Analysis Platform – A user-friendly modeling
platform for improving the productivity of quantitative analysts.
Overview – Advanced Automated trading Systems. Consulting Services –
Helping your quantitative analysts deliver a better product for your
clients. Trading Model Building Services – Continuous and Discrete
Models, using Price or Exogenous Data. Quantitative Analysis Training
Seminars – Topics covered in typical training seminars. Model
Validation – A Catch-22 in the struggle between the Central Limit Theorem and the "Law"
of Requisite Variety.
Non Trend-Following, Non Technical Analysis Methods – The difference
that a non-price market view can make in your portfolio's success. Back to Home
Page © 1997-2004 Thomas W. Wright. All Rights Reserved
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MB_Syllabus.htm
-Loss · Managing Mistakes
Avoiding Common Modeling Mistakes
· Avoiding Improper Market
Assumptions · Avoiding Improper Modeling
Assumptions · Formulating Realistic
Assumptions · Avoiding The Evil of
Curve Fitting (Back-Testing)-- And Some Appropriate Uses for it
· Avoiding the Problems of Linear
Regression-- And Some Useful Solutions
· The "Law"
of Requisite Variety
Versus Statistical Validity ·
Avoiding the Reading of Tomorrow's Wall Street Journal
· Unsupervised Optimization with
Slippage and Stop-Losses Long-Term Issues ·
Eliminating Model Long-Term Bias ·
One Long-Term Model You Must Not Overlook Writing Powerful
Modeling Procedures Without Programming Writing Your Own Mathematical
& Statistical Transformations Is Easy Data Mining Designing A
Quantitative Analysis Platform--Case Study ·
Buying versus Writing Your Own QA Platform
· Selecting a Programming Language
o Scalar versus Array Processing Languages
o Programming Efficiency--System & User
o Allowing "Roll-Your-Own"
Commands and User Functions o Memory Ma
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SHARPE_N.htm
n-stationary, etc. view of the futures markets."meta
name="keywords" content="futures, commodities, risk management,
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predictive, natural gas, s&p 500, treasury bond, energy futures.
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SHARPE_N.htm
s."meta name="keywords" content="futures,
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investments, stock, securities, futures, c
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differen.htm
each with call and put premiums, volume, and open interest. Not the
Usual Moving Average Based Technology All of the foregoing non-price data are
used, together with proprietary transformations (sample graphics), to create
the independent variables used to synthesize a dependent variable (objective
function) using statistical pattern recognition (not chart patterns). The
dependent variable (objective function) oscillates about zero, and is
constructed to trade nearly perfectly. It does not try to trade the noise in
price, so it misses a few trades by design. The synthesis is done with proper
respect for the number of degrees of complexity involved. I do not
"violate" the central limit theorem or the
"law" of requisite
variety (from cybernetics). Not a
Back-Tested Curve Fit I use one of three kinds of cross-validation and am very
conscious of statistical validity issues. I avoid over training, curve fitting,
linear regression, efficient market and random walk hypotheses, and other known
trading system abuses. Since 1986, I have restricted my studies to common
stocks traded on U.S. exchanges (NYSE, AMEX, NASDAQ), fixed income instruments,
currencies, mutual funds, and futures contracts on the S&P 500, US Treasury
Bonds, Crude Oil, Natural Gas, Heating Oil, Euro (Deutschemark, Swiss Franc),
Japanese Yen, British Pound, Gold, and Silver. I have a healthy respect for
options and, though using option data, my technology does not embrace option
strategies, option pricing, or "extreme" derivative products.
(Probably) Not Correlated to Your Portfolio My goal has been to help smooth out
portfolio equity curves by contributing non correlated equity curves which
lower the co-variance of the portfolio. Risk Management involves at least that,
but much more. I diversify at the raw data level (different inputs
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statvali.htm
mployed by those among us who choose to be in this business of building
automated trading systems. It behooves each of us to maintain in our minds the central question of this occupation: "Can I be
statistically confident that the system on which I am working, including its
parameters, is within the population of profitable systems?" Or asked
another way: "Can I reject the null hypothesis that these trading results
could have been achieved by chance?" The Demands Of Complexity Versus The
Demands Of Statistical Validity The demands of complexity are always in a tour
de force with the demands of statistical validity. The demands of complexity may
best be described by the Law of Requisite Variety from
cybernetics. The law of requisite
variety demands that an order-n problem require
an order-n solution. For example, if you are driving on the freeway and run out
of gas you have an order-1 problem. If you pull off onto the shoulder and blow
out a tire, you now have an order-2 problem. Only an order-2 solution will get
you going again. A not-flat tire won't do it. A can of gas won't do it. It will
take both a tire and some gas to fix your order-2 problem. This law suggests that since a market is a non-stationary
process, nothing less complex than a non-stationary process can model it.
Consequently, I view the solution to be a "non- stationary process"
rather than an indicator, model, algorithm, or black box. Let's say that you
have correctly concluded that there are 10 essential forces driving the price
and systemic non-stationarity of IBM common stock. Let's further say that you
have isolated the 10 differential equations, which together describe the stock
market, technical stock and computer sectors, and the economic conditions over
the past year. Let's say that your model trades IBM perfectly with that model,
trading 25 times over the year. You are exceedingly happy. You start t
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statvali.htm
tly concluded that there are 10 essential forces driving the price and
systemic non-stationarity of IBM common stock. Let's further say that you have
isolated the 10 differential equations, which together describe the stock
market, technical stock and computer sectors, and the economic conditions over
the past year. Let's say that your model trades IBM perfectly with that model,
trading 25 times over the year. You are exceedingly happy. You start trading,
but suffer significant drawdown. Q: What happened? A: Your view of the problem
solving domain was inadequate. Though you satisfied the demands of complexity,
you failed to satisfy the demands of statistical validity. The central limit theorem, stolen by the statisticians from the
mathematicians, says that for our tenth-order solution to adequately explain
the market forces, it must have sufficient data. It must demonstrate that of
all of the possible solutions, ours is actually from the population of valid
solutions. Over my 17 years studying this problem, people have brought many
trading systems to me which seem to trade well. They tout them as having been
back-tested over 10 to 15 years, "therefore, they must be OK." I have
had to explain to them that it is not the years of data, but rather the number
of buy/sell trading decisions which are made along the way that is important.
These would-be trading system builders usually do not have a clue about the
subject of "degrees of complexity," which in this discussion I will
call "degrees of freedom." I use "degrees of freedom"
rather than "degrees of complexity" because, while the problem being
solved may be measured by its complexity, problem solvers tend to curve fit
problem by adding more and more "free parameters" into their
solutions. A degree of freedom is frequently associated with each
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statvali.htm
des 2 times each month, then I need to validate it over at least 4 years
of data. Or, if I am considering an indicator which has 2 degrees of freedom,
and I only have 2 years of data, then the indicator must trade at least 2.6
trades per month to be considered statistically valid. The formula for each
entry in the table is TPM = (30*DOF) / (252*NYears/22). In our order-10
solution we, consequently, needed 300 trades and only had 25. That's at least
one explanation for its failure. So, one tries to lengthen the test data in
order to simulate more trades, only to realize that the 10 equations don't work
any more at all. But, the years of data required to avoid "violation"
of the central limit
theorem would span qualitatively diverse market
periods. The Catch-22 If one uses enough data to be statistically valid with a
useful level of confidence, the discriminating variables will come and go like
tax strategies. We are forced to conclude that there can be no closed form
solution. If there can not be an exact solution, then one can only attempt to
emulate a solution, while keeping degrees of freedom, total trades, and trading
frequency under control. [Don't try to understand this paragraph on first
reading. Just skim to the next paragraph.] Predictive models must treat an
idealized price/time series (an objective function) as the output of a
non-linear dynamical system whose structure may be discovered directly or
synthesized. That is, an indicator or model can at best emulate the solution as
an adaptive process. The adaptive process by definition will have a half-life
and consequently must require a smart analyst to keep it on track. The
"half-life" comment is usually true if the input data is exogenous to
price, in which case the losses may be serialized. Sometimes, if the input data
is price, the algorithms used to produce
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techsumm.htm
bsp; Non-price-based (cannot be trend-following) indicator inputs.
· Buy/Sell indicators are a
function of volatility, basis, option, inter-market, sentiment, volume, open
interest, monetary, and other data which is exogenous to price. Statistical
Principles Observed · Proper
handling of time series relative to the number of degrees of freedom involved.
· Balance maintained between
the demands of complexity (the "law"
of requisite variety)
and the demands of statistical validity (the central
limit theorem).
· Cross-validation is achieved
to further ensure statistical validity.
· Over training, curve fitting,
and other known trading system abuses are avoided. ·
Sharpe Ratio used as a risk-adjusted measure of return. Appropriate Exploratory
Tools Employed · Heuristic
(exploratory) tool kit used (over 250 different commands).
· Statistical Pattern Recognition
(not chart patterns) finds weak signals in noisy data.
· Sophisticated mathematical
and statistical modeling language.
· Tracking of parameter sets as
they migrate in parameter space.
· Indicator parameter sets are
constructed to adapt over time or to market impulses.
· &nb
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