IntelliTrade, Inc.
MAPs as Representations of Market System Dynamics
IntelliTrade has developed proprietary pattern representations called MAPs
to model market dynamics. MAPs are distant cousins of artificial neural networks
(ANNs). Like ANNS, IntelliTrade's MAPs are descended through several
generations of innovation from Perceptrons, which were single-layer ANNs
developed in the late 1950s and 1960s to model human pattern recognition.
A MAP of a single time series can be shown as a topographical picture, and
four are included here. The first three pages of graphics show how three different
statistical patterns in time series are represented by IntelliTrade's MAPS. The three
statistical patterns are (1) a random time series, (2) a mixture of four periodic
(sine) time series of different frequencies, and (3) a Mixed Logistic series, the
outputs of several logistic equations summed together to create a complex time
series resembling a real market. The fourth page shows an actual market’s
representation, the 10-year U.S. Treasury Note future.
The graphics are three-dimensional topographical representations of MAPs.
An ordinal measure of time derived from calendar time according to proprietary
transformations runs west to east, a measure of the market's price runs north and
south, and a measure of the market's dynamic behavior creates the vertical
topography represented by the red and green colors.
All four graphics shown here are single-market MAPs and are intended
only to illustrate the fact that IntelliTrade’s market representations can
discriminate among time series with different statistical characteristics.
IntelliTrade’s technology is normally used to MAP the relationships within a web
of related markets, and multi-market MAPs of those webs form the foundation of
IntelliTrade’s trading programs. We do not use single-market MAPs in trading.
The dynamic structure of a time series is embodied in the topography of its
MAP. A random series produces a simple featureless topographical pattern. A
periodic series produces a MAP with clearly separate red and green areas with the
dominant periodicities visible in the MAP’s topography. Both the Mixed Logistic
series and the Treasury Note series show distinctive west-to-east topographical
features that resemble ridges and valleys. Those features represent persistent
aperiodic behavior, and our programs use those features to anticipate future market
behavior to drive trading.
Random Time Series
106
104
102
100
98
96
94
92
90
1
188
375
562
749
936 1123 1310 1497 1684 1871 2058 2245 2432
MAP of Random Series
IntelliTrade, Inc.
2
4 Mixed Sines (Detail)
130
120
110
100
90
80
MAP of 4 Mixed Sine Series
IntelliTrade, Inc.
3
Mixed Logistic Time Series
MAP of Mixed Logistic Series
IntelliTrade, Inc.
4
2401
2201
2001
1801
1601
1401
1201
1001
801
601
401
201
1
110
105
100
95
90
85
80
`
TY Near Month Future Settle
115
110
105
100
95
90
85
80
MAP of 10-Year Note Series
IntelliTrade, Inc.
5
Trading the MAPs
Our programs extract forecasts from a set of MAPs by comparing the
current state and recent past behavior of a market system with the information
stored in the MAPs. As noted above, we do not trade on the basis of a singlemarket MAP. Actual markets are embedded in a web of related markets and
information from the related markets is necessary to drive reliable trading.
Nevertheless, the MAP of a single time series carries information about that
series to the extent that internal dynamics drive its behavior. Therefore, FOR
ILLUSTRATION ONLY, we used the four MAPs above to ‘trade’ their
respective time series, generating cumulative “returns” curves. The trading rules
used to trade the four MAPs are the simplest imaginable: For each day, if the
current signal from the MAP is above some positive threshold be long; if it is
below some negative threshold, be short; else be flat. The results of that ‘trading’
is shown on this graph. The vertical scaling is irrelevant - the data were rescaled
to separate pairs of curves so their shapes are visible. There are 2,180 total trading
days on the graph, with the last 500 days being Out-of-Sample for all four curves.
The first several hundred days of the data series are dropped because the MAPs
require them to make an initial forecast.
IntelliTrade, Inc.
6
Several features of the cumulative curves are of interest. First, the Random
trading shows that our programs can “learn” a random series, but not surprisingly,
there is no generalization at all to novel data. The Random cumulative curve goes
flat at the transition from Training data to Out-Of-Sample data. A random time
series has no internal temporal structure that can be exploited to forecast new data.
The fact that a Random series can be learned very well in Training implies that
great care must be taken to avoid over-fitting when building MAPs for real
markets and that stringent generalization tests are necessary.
Second, the 4 Sines curve shows that our programs can learn a complex
periodic series very well and that they can use what they have learned to
generalize seamlessly to new data. There is no break from Training to Out-OfSample data in the cumulative curve produced by the 4 Sines ‘trading’. If markets
were periodic or quasi-periodic, as many technical analysts appear to believe, our
MAPs would have no trouble modeling them. However, with interesting
exceptions that are associated with strongly seasonal markets, MAPs of actual
markets show no periodicities like those visible on the 4 Sines MAP.
Third, the Mixed Logistic and actual 10-Year Note (TY) cumulative curves
are very similar in their general appearance, with volatility overlaid on a generally
upward trend that extends from the Training period through the Out-Of-Sample
data. That says that our programs can extract whatever autonomous dynamics
there are in a time series and can utilize that information to anticipate likely future
behavior in Out-Of-Sample data. Once again, we would not trade the 10-Year
Note on this single-market MAP: it is too volatile. Our production trading
programs incorporate information from several related markets in order to create
more reliable forecasts for trading markets. Nevertheless, the TY cumulative
returns curve shows that the MAP has captured information about the autonomous
dynamics (“technical” properties) of the 10-Year Note’s price stream, and that
information does enter our actual trading programs along with other information.
Finally, consistent with what we have learned over a decade of research in
modeling markets, there is a subtle indication on the graph suggesting that a fair
amount of past data is necessary for the MAPs to learn the dynamical properties of
a market price time series. Both the Logistic and TY curves are fairly flat in the
first half of the Training period – there is not enough historical information early
in training for the MAPs to learn the internal dynamics of the two time series. As
training proceeds through time, though, the cumulative curves begin to climb,
indicating that with more training data the MAPs come to embody more and more
information about the dynamical structure of the time series. That is especially
true for the Mixed Logistic series, which is driven solely by internal dynamics.
The 10-Year Note is subject to influences from the outside world, and thus its
internal dynamics are only part of what drives its price.
IntelliTrade, Inc.
7
Adaptation
Adaptation is a significant issue in modeling markets. Markets are complex
adaptive human social systems. As external conditions change and as market
participants learn new behaviors, market dynamics evolve through time rather than
remaining static. It is therefore necessary to design market representations that
can learn as the markets they represent evolve. Adaptation must occur frequently
enough to avoid missing significant changes in the dynamical system, but not so
frequently as to ‘adapt’ to transient noise. The rate of adaptation must be
appropriate to the time grain(s) of the systems that the program is to model.
IntelliTrade’s programs are designed to provide information over time horizons
ranging from five to thirty future trading days utilizing from 100 to 300 days of
recent past behavior to produce their forecasts.
Adaptation in IntelliTrade’s programs occurs mainly through retraining on
new data. The MAPs for a given market system or web are originally trained on a
fair-sized sample of past history, on the order of five years or more. That training
establishes the MAPs’ original “knowledge” of the dynamics a market system has
displayed during the training period. Thereafter, MAPs are retrained at intervals
of approximately a year. In effect, the retraining overlays new market system
behavior on top of an existing MAP, reinforcing recurrences of old dynamic
modes and adding information about new modes if they have occurred.
One might suppose that feedback of recent forecast error would play a role
in determining the frequency of retraining in some markets, but we have found in
extensive testing that retraining MAPs at frequent intervals is at best a waste of
time and at worst encourages spurious adaptation to transient conditions and/or
noise. Absent substantial changes in market system conditions (for example, the
1992 breakdown of the ERM), if a MAP is trained on a sufficiently deep historical
sample, retraining is rarely necessary.
We have evidence to suggest that the markets we work with display a finite
and quite limited number of different dynamical regimes, and once a MAP has
learned all of those regimes, retraining is rarely necessary. However, since the
events that create substantial changes in market dynamics or that create a new
dynamic regime are often known only in hindsight, we retrain and retest our
MAPs at least once a year regardless of whether we think a genuinely new
dynamical mode has occurred. If changes in market system dynamics have
occurred since the last retraining, the MAP will learn the new dynamics; if they
have not, it will learn nothing new in retraining and will continue as before. The
adaptation issue continues to be an area of active research, though, and our
procedures for it may change.
IntelliTrade, Inc.
8