Statistical
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Statistical Validity of
Non-Trend-Following Technologies In Non-Stationary Markets 2; Statistical Validity of
Non-Trend-Following Technologies For Automated Trading Systems In
Non-Stationary Markets. I am at once amused and saddened by the lack of statistical rigor employed 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.
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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
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into their solutions. A degree of freedom is frequently associated with
each free parameter in a simulated trade history. They usually have used far
too many degrees of freedom in their models to be statistically
valid. Most statisticians would demand 30
decisions for each degree of freedom (DOF). In the body of the above chart are
the number of trading decisions / month which are required for indicators or
models with from 1 to 6 degrees of freedom simulating trades over from 1 to 7
years. For example, if I am building an indicator with 3 degrees of freedom,
and it only trades 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. Someti
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trader) that crosses through zero from negative to positive every time
one would like to buy, and which crosses through zero from positive to negative
every time one should to sell. Then, one may use statistical
pattern recognition
techniques (not chart patterns) to locate data
(independent variables) which can be used to synthesize or emulate that perfect
trader or objective function. If, during the process, one keeps close reign
over the degrees of freedom, one might emulate the oscillator such that the
process is statistically valid (in which case it
is expected to make money). Also, if the process is designed with adaptation in
mind, one can tune it periodically (in practice - weekly) and keep it working.
The process is non-linear over the long term, but parts of it are
maintained/treated as if they are locally linear. Using the above techniques,
one may satisfy both the demands of complexity and the demands of statistical validity. Of course, the usefulness of the
resulting indicators will be a function of (1) the information content of the
data chosen for independent variables, (2) the efficiency of the noise
reduction employed, and (3) the ability to discern a buy/sell decision in data
which invariably has a low signal-to-noise ratio. Statistical
Pattern Recognition
Statistical pattern
recognition is that body of science, popularized in the 1980s by the
American and Soviet navies, which almost totally eliminated submarine prop wash
noises, detectable by enemy sonar. They got props to be so quiet that the
largest amount of recognizable noise was coming from the galley cooks yelling
at each other. Neural nets helped those studying this problem to realize that
the remaining noise was coming from people. They then replaced the cooks with
microwave ovens and frozen meals. But that's another story. We got a glimpse of
that story in the movie "Hunt for Red October." Remember, they were
huddled over the sonar, wondering if the noise on the screen was from an enemy
sub or a whale. Among other technologies, they were using statistical pattern recognition. Pattern recognition is
that discipline which recognizes structure in seemingly chaotic noise. There
may be information in a time series, but it is covered by the noise. The
signal-to-noise ratio is very small. The information about how many people
stick with their positions overnight is very obvious in open interest data. But
the very numbers telling us that information are themselves almost all noise,
IF one is interested in whether one should be long or short. Noise frequently
dominates the data, especially if one is looking at a short planning horizon
and at price or volume data. The signal-to-noise ratio is quite small for that
information. But it is there. And it takes statistical
pattern recognition technology to find it. (It does not find much
buy/sell information in price data.) To find information in a sea of noise
requires two essential operations: noise reduction (or filtering) and statistical analysis. I have a mathematical
transformation which removes noise (with excellent frequency response), which
works with fractional days (moving averages only work with integral days), and
delivers a well-behaved (oscillates about zero as does the perfect trader I'm
trying to emulate) derivative surrogate of the time series. The best part is
still to come - it does all that and only adds ONE degree of freedom to my
solution (requiring only 30 trade decisions). I have another statistical evaluation algorithm which can do a good
job of both analyzing an input stream and converting it to a very well-behaved
oscillator (hence it generates a trading signal) and it only adds ONE degree of
freedom. Using those two together, I can take most data inputs and test them
against my perfect trader, while keeping the degrees of freedom to only TWO or
sometimes THREE. This means that I can emulate the perfect trader, generating
more than 60 to 90 trades, and keep the total length of the training period to
a year. That is, it will have to trade from 5.2 to 7.9 trades each month to be statistically valid with 2 or 3 degrees of freedom and
a year of data. The feat is somewhat remarkable. Unfortunately, the
profitability has declined over time due to the non stationarity and increased
volatility of the markets. Pity the analysts using systems which combine
stochastics (with 1, 2, or 3 DOF) with moving averages (1 or 2 if crossing MAs
or MACDs) and with additional rules (which each add 1 DOF). Those may have to reverse
almost daily and work over 2 or 3 years to be considered statistically valid. And we all know how the markets
can be qualitatively different over two years. I worked at a company which
traded a 2-bullet system (stochastics and bandpass filters) with rules which
had 15 degrees of freedom. My job was to validate their system. It didn't have
a chance of making money. Cross-Validation The final step in the quest for statistical validity involves Cross-Validation.
Cross-Validation is a statistical procedure used
to avoid the problem of "over-fitting" the data. Since many statistical patterns
that appear to be useful are not real but rather "fools gold."
Cross-validation sometimes involves the sequestering of input data into two or
(usually) three sets -- (1) a learning set, (2) a testing set, and (3) a
validation set. The three sets are subjected to successively harsher
examination. Tests are performed to determine if parameter sets can migrate or
adapt within and among the three test data sets. The obvious objective is to
reject bogus statistical relationships before
trading assets are lost. Too frequently, either the market non-stationarity or
the lack of data is a problem. The market non-stationarity problem may be
attacked by an adaptive walk-forward model. The lack of sufficient testing data
problem may be attacked by a "vertical" approach. That is, using
varying sources of input data over the same short time horizon in order to
increase the number of independent trading decisions. This process is especially
useful for trading newly created sector funds, where parameter sets may be
found that can trade the dominant stocks within the sector, and added together
can trade the fund profitably. The Importance of this Website
to Your Business As the markets become more volatile, you would do well
to train your quants to protect your portfolio against the ill effects of
nonstationarity. Exogenous Data Based Models The good and bad
characteristics of Exogenous Da
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equency, indicator, model, market instrument, and portfolio).
· Is risk averse.
· Is statistically
valid. · Trades
consistently over time. ·
Functions across diverse instruments: Futures; Equities; Mutual Funds; Options;
Fixed Income; FOREX; Precious Metals Correct Market Assumptions Maintained
· Markets are non-stationary
(structure underpinning the markets is evolving over time).
· Market forces are non-linear.
· Parameter set usefulness
decays over time requiring an adaptive solution.
· Efficient market theory &
random walk hypotheses have been discredited and rejected. Indicator Research
Domain Well-Defined · Robust,
self-adaptive, non-linear, statistically valid,
predictive indicators. ·
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.
· Comprehensive tool kit
promotes statistical validity. The Importance of
this Website to Your Business As the markets become more volatile, you
would do well to train your quants to protect your portfolio against the ill
effects of nonstationarity. Exogenous Data Based Models The good and bad
characteristics of Exogenous Data. (Dont miss the interesting visualization of
some SPX Index Option data.) Visualization of Exogenous Data In case you
missed it above. 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
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esent technology in many ways I help increase your portfolio's capacity:
The above technology diversification increases portfolio capacity while
reducing performance volatility. Improving the statistical
validity of your portfolio's models While price data at end-of-day only
includes open, high, low, close, and volume data (only 5 data values). One of
the intractable problems with such price data is the requirement for long
periods of time to achieve statistical validity. Cross-validation of models requires lots of
data. Alas, such long periods of time frequently include nonstationary market
movement which is disruptive to one's search for model parameters. On the other
hand, exogenous data may have thousands of data values covering the same single
day, addressing the same market, and provided by some of the smartest market
participants. The availability of that remarkable quantity of non price data
values can contribute significantly to the statistical
validity of your models. (Read more about this in the next section.) I
help your database staff to stop missing predictive data on your data feed: We
organize the collection of exogenous data I help your systems staff to improve
your modeling platform: Make the testing of new ideas easier Add
noise-reduction transforms with less lag and better frequency response Better
graphics (sample 1; sample 2; sample 3 ) I help your Quants to avoid crucial
model building mistakes: Avoid statistical validity
problems with proper cross-validation Deal with non stationarity of markets Avoid
looking at tomorrow's WSJ Recognize the problems of traditional statistical calculations in a trading
environment (e.g. Linear
Regression)Avoid overlooking market inefficiencies I bring 20 years of
automated trading system modeling experience to the table: I Understand the
difference in reactive data and predictive data My models adapt to non
stationary markets I teach 3-day or 4-day Seminars to Quants I demonstrate the
above with a superior Quant Workstation The
Importance of this Website to Your Business As the markets become more
volatile, you would do well to train your quants to protect your portfolio
against the ill effects of nonstationarity. Exogenous Data Based Models
The good and bad characteristics of Exogenous Data. (Don't miss the interesting
visualization of some SPX Index Option data.) Visualization of Exogenous
Data In case you missed it above. 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 Validatio
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noise reduction and outlier detection and repair; Functions for making
de-noised but nevertheless ill-behaved input data into well-behaved, smooth,
and normalized oscillators; Statistical
evaluation functions; Buy/Sell signal generators; and Model synthesizing
functions. Trading indicators are built from the many combinations of the
foregoing types of mathematical and statistical
transformations, while using an infinite number of possible parameters that are
associated with such transformations. Usually, as more transformations are
introduced into an indicator, more ill effects are also introduced: lag,
curve-fit, poor performance, and lack of statistical
validity. The ideal transformation would be one which has only one free
parameter and is capable of de-noising the data, making it into a well-behaved
oscillator, and firing buy/sell signals with minimal lag.
The minimum quant toolkit is a collection of subroutines that can
be employed to build statistically valid trading
indicators. As quants investigate new ideas, the functions resulting from them
should generally go into the toolkit. It is imperative that there
be an ability to develop and test new transformations with minimal effort. How
much more productive would your quantitative analysts be if they could explore their
own quantitative market ideas without delay? Training
Quantitative Analysts In this context, "quantitative analysis"
involves the building of sub-indicators and indicators, and the combining of
them into trading models. We are not concerned with the financial engineering
aspects of combining market instruments into exotic derivative products or in
the pricing of options. The building of robust trading models can be
quite time consuming; focusing management attention on analyst productivity can
become one of the most important issues.
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trading system design experience. Applied Market Analytics,
Inc. offers quantitative analyst training at your location and adapted to your
needs. We will use a sophisticated quant workstation
to demonstrate how your infra-structure could help your quants to become more
productive. Diversification Our goal, in part, is to help managers
to improve their portfolios' performance through diversification. Traditional
diversification mostly involves the inclusion of additional trading instruments
from multiple markets. But besides trading instruments, diversification can be
enhanced in other ways--even within the component sub-indicators, indicators,
and models. The purpose of additional diversification is always to improve the
covariance of the overall portfolio. Some examples of the many different
ways of achieving additional portfolio diversification, using the trading of
the S&P 500 Index as an example, might include: Constructing
indicators from data that are exogenous to the market being traded (e.g. NASDAQ
100, MID CAP, Russell 2000, U. S. Treasuries, & VIX); Constructing
indicators from data that are exogenous to price
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models; Adding diversification of technologies (e.g. both continuous and
discrete models); Pre-processing indicator input data with mathematical
transformations (e.g. various statistical
functions which remove outliers, scale, de-trend, discretize, or otherwise
normalize the input data); Transformations for removing noise (e.g. exponential
smoothing, open interest expiry removal, log, proprietary noise-reduction
functions); Mathematical transformations for converting ill-behaved input time
series data into well-behaved oscillators about zero (e.g. least squares slope,
derivatives, MACD, creation of objective functions, etc.); Generating
Buy/Sell trading signals at varying trading frequencies from processed
indicators (e.g. daily, n-days, weekly, monthly); and Combining indicator
trading signals into models (e.g. screens, allocation size as a function of
various measures of "good," etc.) Diversification of technologies
will sometimes allow trading in markets during which single technology trading
systems are on the sidelines. Would it be a serious setback to your clients if
you
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signal to-noise ratios are almost always very low. That is, the signal
information about the future direction of price is swimming in a sea of
noise. It is necessary to use mathematical and statistical
transformations to filter or remove the noise and thereby expose the
information in the data. The simple moving average (a statistical
transformation) is frequently used by technical analysts to filter day-to-day
price fluctuations (noise), leaving a time series which more clearly depicts
the market trend (information). We are not interested in determining trends
because the resulting number of trading decisions is usually insufficient for statistical validity purposes. We are interested in
exposing buying or selling opportunities. Over eighteen years, we have used
mathematical and statistical transformations on
many market data time series. Many combinations have produced trading signals
which seem to perform well but do not pass our rigorous statistical validity tests. Failure is usually due to (1)
insufficient trading activity relative to the number of degrees of freedom, and
(2) inability to withstand rigorous cross-validation tests. The types of data
which repeatedly pass the statistical tests
include those indicated on the Causality Spectrum depicted above (and several
more). It is interesting to note that the most useful data is not the easiest
data to obtain. The resulting trading systems implemented by AMA are not
traditional forecasting, technical analysis, reactive, breakout, cycle
analysis, trend-following, or any other price-based systems. My technology
might be more correctly characterized by the term "threshold analysis"
or "set-up condition analysis." My technology begins with the belief
that to have superior performance, while being qualitatively and quantitatively
different, market timing decisions must be predictive rather than price
reactive. To be predictive requires a market model which indeed performs well
over past history and can be "executed" for tomorrow's market. It
should be pointed out that causal relationships, even when intuitive, are
rarely linear and not easily visualized.
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e%20to%20You.htm
cause havoc to the market modeler. The shorter the timeframes, the less
market data one has with which one may train. Moreover, the less market data
one has, the more difficult it is to establish statistical
validity. There are techniques which can help to
maintain statistical validity. Switching from
traditional linear cross-validation to vertical or walk-forward cross-validation
techniques may save your model. So, if (a) your models are not performing as
they used to perform, (b) your quants are spending increasing amounts of
valuable time attempting to keep them "tuned," (c) you wish to
diversify your technology, or (d) your technology does not incorporate
exogenous data, then consider protecting your investment in people and
technology with some continuing education. They
Need A Sophisticated Quant Workstation. It is
likely that you have a quant staff capable of doing their own programming. This
is important. They are probably programming with "C," Visual
Basic, Matlab, Mathematica, or Excel. They may already be using a quant workstation. Seminars taught by Applied Market
Analytics, Inc. use a proprietary Quant Workstation
and Quant Command Language ("QCL"). The QCL is unique, in that it
offers a complete range of database access tools, user friendly commands,
powerful mathematical transformations, statistical
functions, and optimization facilities. Furthermore, it allows your quants to
write and incorporate their own mathematical transformations to exploit your
proprietary data and ideas, resulting in models that are uniquely yours.
Your Quants Need A Productivity Tool of Thought. Quant productivity is
often diminished by the time lag between the origination of a modeling idea and
the testing of that idea with actual market data. The QCL allows quants to test
most ideas as they occur, using a set of over 1200 user commands.
Additionally, an extremely efficient high level language allows them to program
new transformations with great ease, making their own commands. Programming new
transformations and new commands "on-the-fly" does not require the
compiling, linking, and reloading of data time series. One can originate new
commands, incorporate them into the Command Language system, and begin using
them without shutting down or restarting
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most would be competitors for exploiting the inefficiencies therein;
6. Inefficiencies in seldom used data tend to remain exploitable for
longer periods, i.e. models work longer; and Statistical
validity is never a problem because of the quantity of information
present every day. Click HERE to see how the above can be developed into a
Trading Strategy. Exogenous Data Based Models The good and bad
characteristics of Exogenous Data. (Don't miss the interesting visualization of
some SPX Index Option data.) Visualization of Exogenous Data In case you
missed it above. 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
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using advanced vector and array processing techniques, is the primary
goal of the QCL. Consequently, the QCL facilitates the use of
mathematical time series transformations, sophisticated statistical and mathematical analysis tools, portfolio analysis
tools, market indicator, model synthesis, and signal generation commands,
non-linear optimization tools, database management commands, and trader support
facilities. The system allows market analysts to explore market dynamics
heuristically, build indicators, walk the indicators through non-stationary
periods, test indicators for statistical validity, integrate them into market models, and
actually trade the models in daily operations without re-programming them. The
QCL also provides tools to help the analyst to write new commands easily
without the compile-link-execute cycle, to test them at will, to write and
execute procedures using these commands, to maintain a data base of data
vectors and procedures, to mine extensive databases for market inefficiencies,
to execute vendor programs from within the QCL and use their results, and to do
almost anything that computers do in a very friendly environment.
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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 for
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premiums, volume, and open interest for Calls and Puts · Collect
metrics into historical time series (vectors) · Use statistical pattern recognition and vertical
cross-validation techniques to identify and validate automated trading signals
generated from the vectors. The concept is simple, "Instead of
waiting for price data to indicate direction of trend, use today's sentiment of
the option traders, as encoded in the option chain, to indicate market
direction." If one is interested in trading a Sector, or a Market Neutral
(or Long/Short) basket of Sectors, then, one simply
· accumulates the normalized metrics
for a weighted representative group of stocks (e.g. see Rydex's weights for its
holdings for its Health Care Fund); OR
· generate trading signals for each
representative stock for the sector (with signal magnitude), and accumulate the
weighted signal magnitudes. Implementing ideas, such as the above, has been the
focus of my consulting practice for many years. Please browse around my website
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gnal Generation Objective Functions Signal Generation TA Oscillators
Signal Post-Processing Model Synthesis Discrete Modeling Trade History
Simulation Accounting & Statistics Equity
Curve Management Reporting Profit Matrix Example Statistical
& Curve Fitting Vector Statistics
Curve Fitting Vector System Statistics User
Procedures / Scripts Editing User Procedures Executing User Procedures
Importing & Exporting User Procedures Documenting User Procedures Control
Structures Graphics Basic Graphics Advanced Graphics Auxiliary Graphics
Graphics for Options Parameter Optimization Iteration Commands Indicator
Diagnostics Diagnostic Tools Profit Matrix Example Writing and Managing
Your Own Commands Command Management Function Management
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cs, Algorithm Robustness, Alpha Cycle, Alpha Cycle Trading, Applied
Market Analytics, Array Processing, ASCII Time Series, Automatic Trading
Systems, Back-Office Accounting, Basic Graphics, Basic Statistics,
Basis, Block Trades, Browsing Vectors, Buy Sell Signal, CFTC, Calendar
Maintenance, Character Arrays, Character Strings, Chebychev Polynomials,
Cluster Analysis, Combinatorics, Combining Trading Signals, Command Syntax,
Commodity Futures Trading Commission, Commodity Trading, Compare, Composite
Graphics, Constrained Regression, Consulting Services, Conventions, Convert
Character to Numeric, Convert Number Base, Convert Numeric to Character, Cross
Rate, Cross Validation, Cross-Validation, CSV Files, Cubic Spline, Currency
Cross Rate, Current Indicator, Curve Fitting Functions, DDE Interface, Daily
Model, Data Acquisition, Data Base Access, Data Base Commands, Data Scrubbing,
Data Types, Data mining, Date Functions, Date Management, De-Lagging, Degrees
of Freedom, Development Tools and Approach, Diagnostics, Direct Delta/Impulse
Functions, Discrete Modeling, Discretization, Disk Directory, Diversification,
Documentation, Draw Down, Drawdown, Econometric Data, Editing,
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ement, Procedures with Arguments, Profit Matrix, Profit Matrix Reporting,
Profit Retracement, Prompt for Input Data, Psychology of the Market, QCL, QCL
Session, Quant, Quant Command Language, Quant Workstation,
Quantitative Analysis, Quantitative Analysis Platform, Quantitative Analysis
Training, Random number generation, Random Vectors, Random Walk Hypothesis,
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Volatility, Walk Forward, Windows Functions, Writing Procedures The Importance
of this Website to Your Business As the markets become more volatile,
you would do well to train your quants to protect your portfolio against the
ill effects of nonstationarity.
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www.appliedmarketanalytics.com/QCL/history.htm
on developing a trend-following futures trading and risk management
system that did not work very well. We had an elite "rocket science"
staff of 33 people, including PhDs, mathematicians, statisticians,
and several genius caliber scientists from NASA, IBM, Rice University, etc. But
our R&D efforts were essentially in vain: our resulting systems were
influenced by wrong market assumptions; we were working in the wrong problem-solving
domain; we violated subtle statistical
principles and cybernetic laws; we were using exploratory tools which looked
great but were incapable of the task; and we were convinced that the holy grail
was ours for the expenditure of just one more million dollars. Fortunately, the
organization disappeared with the S&L industry, we lost the rights to our
"technology," and I was personally forced into a completely different
market / scientific mindset. Since then, I have been helping risk managers
avoid those expensive mistakes. During the following nine years we corrected
all of those errors. I helped change the R&D direction to embrace
appropriate market assumptions. We moved from the linear to an adaptive
non-linear domain. We developed our own sophisticated mathematical and statistical modeling tools. I even re-wrote some basic
statistical formulae to operate in this domain.
We developed a statistically valid exploratory
tool kit which set a new standard for others to follow. And now, I have
completely re-written the quant workstation as a
fully integrated platform. It is altogether different from traditional
fundamental, cycle, or technical analysis based technologies. It was this
approach that was worthy of the attention we received from the blue chip companies
mentioned above. The equity curves that result from a non-trend-following
technology can reduce the co-variance of and thereby improve the performance of
a proprietary trading portfolio. It can be an exceptional way to reduce the
overall risk of your futures portfolio. The Importance of this Website to Your
Business As the markets become more volatile, you would do well to train
your quants to protect your portfolio against the ill effects of
nonstationarity. Exogenous Data Based Models The good and bad
characteristics of Exogenous Data. (Don't miss the interesting visualization of
some SPX Index Option data.) Visualization of Exogenous Data In case you
missed it above. Quantitative Analysis Platform
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www.appliedmarketanalytics.com/QCL/indic2.htm
and guesses and moods, rational and irrational, of hundreds of potential
buyers and sellers, as well as their needs and their resources -- in total,
factors which defy analysis and for which no statistics
are obtainable, but which are nevertheless all synthesized, weighed and finally
expressed in the one precise figure at which a buyer and seller get together
and make a deal. This is the only figure that counts. [emphasis added] This writer
does not disagree that "price reflects" all. The issue lies in the
words "finally expressed..." Price IS an EFFECT -- NOT a CAUSE.
Therefore, any system based on price is reactive -- not predictive.
Consequently, we do not use price, per se, as an input to our market
indicators. In no way should this discussion be construed as anti-technical
analysis. There are more trend following systems in use today, making more
money, than any other type of system. That is precisely why there is such a
great opportunity for non trend followers. The issue at this web site is Risk
Management By Being DIFFERENT. Adding non trend following, non technical
analysis, non price based, non stationary, non linear equity curves to an
existing portfolio can help
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www.appliedmarketanalytics.com/QCL/indic2.htm
is an altitude which reflects the goodness of an indicator (Z-axis) whose
two principal components are the variables noted on the X- and Y- axes. Along
the X-axis are parameters of a proprietary statistic,
while the Y-axis depicts parameters used in filtering noise from input data4.
The non-stationary market assumption may be envisioned as a Sharpe Ratio
surface which is moving about over time. Today, a set of parameters xi and yj
may produce Sharpe Ratio zi,j, but a month from now the same parameters will
produce a different Sharpe Ratio z'i,j. Building Indicators which Adapt to Non
Stationarity An indicator may be constructed as follows: First, a raw indicator
time series is created over several years of input data. For example, the raw
indicator time series could be the ratio of the total daily put volume to the
put open interest5 for the options on the instrument for which this indicator
is being built. It was described in Part 1. It is a well-behaved oscillator
before it is used in indicator construction. Being "well-behaved," it
oscillates about zero and is scaled to some reasonable range. It may even have
a mean of zero and a standard deviation of one.
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It may even have a mean of zero and a standard deviation of one. Second,
a univariate filtering transformation is used on the raw indicator time series
to remove varying amounts of noise. Third, a statistical
calculation is performed on the filtered time series producing the final time
series. The final time series is an indicator in its own right which oscillates
about zero, generating buy and sell signals as it crosses through zero. These
signals are used in a trade simulator which calculates the Sharpe Ratio of the
resultant equity curve for each parameter pair. For present purposes each of
these indicators will be called a sub-indicator, reserving the designation of
indicator for a more robust time series made up of several sub-indicators
combined in some useful way. The non stationary market assumption infers that
the Sharpe Ratio surface in the above graph is moving about over time. A point
which is downhill from the peak today may climb up the hill (see footnote 1 in
Part 1) and become the new peak next week. The innovation being described here
involves how the set of sub-indicators, represented by parameter pairs, are
used in the construction of a single more robust
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problem to be "locally linear." This is not a bad idea if one
doesn't apply the idea with abandon. The problems with linear methods go far
beyond the issues of linearity and non linearity. In general, statistical formulae and statistical
tools were not conceived with the futures markets in mind. While statistical validity is absolutely essential and often
neglected, the use of every statistical formula
and tool must be considered with great care. As an example, let us consider
Linear Regression as a tool for synthesizing information into indicators.
Consider that the sub-indicators have been carefully selected as varietal
samples from a robust Sharpe Ratio surface. The points on the surface
represented positive Sharpe Ratios -- not negative. Consequently, let us define
them as right-side-up sub-indicators. It might seem useful to consider using
ordinary linear regression to synthesize the sub-indicators into an indicator,
fitting the objective function in a least-squares sense. But, linear regression
has no conscience. It has one task to perform -- minimize the sum of the
squares of the residuals. In order to do that it will freely assign negative
coefficients. But, if we allow regression to use negative coefficients, we also
allow regression to turn our sub-indicators up-side-down. While this may give a
better curve-fit, it will do so at the expense of predictivity
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www.appliedmarketanalytics.com/QCL/indic2.htm
crosses through zero. And crossing through zero is all that we are
concerned with in the financial markets. This might be less true if our trading
frequency is very low, but that may not be the case. Statistical
validity may require that we trade seven trades each month. Certainly,
the more degrees of freedom we allow in our indicators, the more frequently we
must trade, and the more sensitive our synthesis of indicators must be to when
the resultant indicator crosses through zero. In the extreme case, a very fast
trading indicator which is otherwise perfect, but one day off, may lose every
trade. Furthermore, linear regression does not consider that recent market
action might be more important than distant market action. Regression will
dutifully seek to minimize the sum of the squares of the residuals. If there
are large residuals toward the beginning of your chosen indicator construction
time horizon, regression will do everything in its power to minimize them at
the expense of recent market activity. And fourth, regression will allow one
stubborn (large) residual to lock your indicator into a LONG or SHORT position
until enough time has elapsed for that residual to be dropped
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option expiry had been removed prior to computing this ratio. [6]
Robustness involves many issues, including high Sharpe Ratio, fairly flat
surface, and sufficient trading decisions to be considered statistically valid considering the degrees of freedom
in the optimization process. Here, assuming five or more trades / month, each
year of data should have 60 or more trading decisions, which is 30 decisions
for each of two DOF. For further discussion, see Statistical
Validity. The Importance of this Website to Your
Business As the markets become more volatile, you would do well to train
your quants to protect your portfolio against the ill effects of
nonstationarity. Exogenous Data Based Models The good and bad
characteristics of Exogenous Data. (Don't miss the interesting visualization of
some SPX Index Option data.) Visualization of Exogenous Data In case you
missed it above. 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.
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