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					                                   Rule-Based Expert System
                                                         Dressler
                                                     1272 Pine Circle
                                                   Bellefonte, PA 16823


Abstract                                                         systems – they do not need to learn how to recognize
In this paper, I propose a design for a rule-based expert        patterns. This means that even with a very short stock
system that attempts to maximize profits while playing a         history, we can begin our investments because the ability to
simulated stock market which, unlike in the real market,         recognize patterns is already built into the system as part of
actually contains embedded patterns within the stock price       its expertise.
data. This expert system will use linear regression analysis          Given the problem on hand and the advantages of the
in conjunction with the Stochastic Oscillator to predict         rule-based expert system, this paper will explore a variety
future stock prices. Using these predictions, the expert         of possible solutions, assess their pertinence, narrow down
system will predict which stocks are most likely to yield the    an approach, and then finally lay out the details for a system
highest profit and invest accordingly.                           that will solve the problem.

1.   Introduction                                                2.   Prior Work
     Number crunching is the digital computer's finest (and           Before one can understand the design for the system to
perhaps its only) trait. Not long after its invention, the       solve the stock market problem, one must first understand
stock market quickly became a target of this useful ability.     some of the other systems which preceded it. It is after all
Many techniques have since been refined to sift through the      their work which has brought to light the solution which
incomprehensibly large amounts of data needed to predict         will be mentioned here later. First, this paper will introduce
stock prices. More and more sophisticated systems are            the applicable pieces of other solutions that contribute to
being built as people realize that predicting a future stock     the design of the overall system. Then, the system design
price is not as simple as looking at a graph of the data and     as a whole shall be described, denoting how the pieces are
plotting the next point. The truth is that there are countless   integrated together.
economic factors that influence the real stock price and they
are not always obvious [1].
                                                                 2.1 Rule Standardization
          But let us instead suppose for a moment that
pattern were truly embedded within the stock price data             In developing a stock trading expert system, a large part
rather than being interdependent upon external economic          of the challenge is choosing which rules to use, especially
factors. Then, if provided a complete history of closing         when the rules may come from very different prediction
stock prices, perhaps the next future stock price could          environments. Then, the knowledge engineer must then
accurately be predicted. It seems natural to use the number-     tackle the problem of standardizing these rules in such a
cruncher’s ability to do the job, but how exactly might such     way they may all be compared with one another in a single
a system be built and operate?                                   rule-base. Since several very different components will be
                                                                 incorporated into the system, standardizing the rules
          In addition to there being patterns in the stock
                                                                 becomes very important.
price data, let us also assume that we have $25,000 and that
                                                                    One particular system used 350 trading rules where each
we know in advance how many days we have to attempt to
                                                                 rule was manipulated to return -1 to indicate to sell, 0 to
make a profit. Suppose also that we are provided with a
                                                                 indicate to do nothing, and 1 to indicate to buy [2] Many
fixed number of fabricated stocks (with no prior history)
                                                                 of its other rules returned values falling between -1 and 1 to
and are provided on a daily basis with each stock’s closing
                                                                 indicate some degree of confidence in favor of one
price. Additionally, at the end of each day, we also have
                                                                 direction or the other [2]. The Stochastic Oscillator, Ease
the option to buy or sell stocks, where each trade costs $5.
                                                                 of Movement, and Relative Strength Index indicators were
Given these rules, how should we then proceed to maximize
                                                                 each independently refined to return values appropriate to
our profit?
                                                                 the [-1, 1] scale and were subsequently incorporated into
          A rule-based expert system is a natural choice. It     the rule-base [2]. So, even though the system incorporated
allows for a system to incorporate expert-level knowledge        four different indicators, each of the four indicators were
without having to learn anything. Many rival systems             standardized such that the rules produced values ranging
would implement neural networks or genetic algorithms,           from -1 to 1.
but given the particulars of our experimental situation, rule-      Scaling the output using a methodology such as this is
based system have an enormous advantage over these other         critical. It puts all of the rules on the same playing field
and allows other rules to generically deal with each of the      point in time to sell. Conversely, if the MEL moves below
systems and allow for such rules to depend on one another’s      the MEL, then the current price is undervalued compared to
output in a consistent way even though the rules may have        the real price and so the price will likely increase, thereby
been derived from very different environments. This              indicating a good opportunity to buy.
concept will play a key role in the composition of the              Applying indicators such as these seems fairly straight
system designed for playing the make-believe stock market        forward, but representing such indicators as a rule-set for an
and its pertinence will soon become clear.                       expert system is more problematic. One system which uses
                                                                 Granville’s Law relies on the graph overlaying the MAL
2.2 Using Regression Analysis                                    and MEL together. Once graphed, the rule representation is
                                                                 accomplished using a sort of simple grammar to describe
   Note that the make-believe stock market problem very
                                                                 how a stock’s moving average line (MAL) compares to its
different from the real stock market problem. In the make-
                                                                 end price line (MEL) and also to describe their trends as a
believe stock market problem, stock prices are not
                                                                 whole [4]. For example mal(d(2),o,i(1),b), would mean
influenced by external factors such as quarterly earnings,
                                                                 “The MAL and MEL are decreasing at a rate of 2 (where
projected profits, trading traffic, general market trends, and
                                                                 the MAL is over the MEL) and then increasing at a rate of 1
dividend times. The problem is therefore no longer finding
                                                                 (where the MAL is below the MEL)” [4]. Once the stock
the pattern between stocks prices, the value of the company,
                                                                 price is represented, rules can be applied such as the
and the surrounding economy. The patterns are instead
                                                                 following:
embedded directly within the provided stock-price data.
One challenge in creating such a stock trading system is
                                                                     IF    mal(d(-),o, c, -, i(3), b) THEN buy
therefore finding rules that rely solely on stock price in
order to determine a trend and the momentum in a stock
                                                                    This form of rule representation is fairly straight forward
price [1].
                                                                 and performed fairly well, but this representation is also
   In one case, an expert system used the last 30 S&P index
                                                                 more complicated to implement in comparison to other
values fitted to a formula using a linear regression analysis
                                                                 methods that predict the stock price using similar
technique to quantify what the overall market might be
                                                                 techniques such as the Stochastic Oscillator indicator [1, 2]
doing [3]. In the case of the make-believe stock market,
                                                                 (an indicator very similar to Granville’s Law [4] and
stock prices are not interdependent. However, this presents
                                                                 frequently called the KD-line [1]). Like this particular
an interesting direction – trend analysis using regression
                                                                 application of Granville’s Law, the Stochastic Oscillator [1,
analysis [3]. A formula derived using regression analysis
                                                                 2] uses a moving average line to compute when to buy and
could fit very well to data that actually has embedded
                                                                 sell. However, one problem with techniques such as these
patterns. In fact, such a formula would fit flawlessly in
                                                                 is if, for example, five stock prices that fall on a line and are
cases where the stock price pattern were in fact linear.
                                                                 steadily increasing, the Stochastic Oscillator indicator [1, 2]
Since regression analysis is a powerful instrument for
                                                                 will continually signal to the system to sell, even though
predicting trends in stock data, it will be used on a per-
                                                                 common sense might say to buy because of the upwards
stock bases and ultimately be the most important piece of
                                                                 trend. Indicators such as the Stochastic Oscillator indicator
the system designed to tackle the make-believe stock
                                                                 [1, 2] clearly do not recognize trends in the stock price data
market problem.
                                                                 (hence the reason why the Stochastic Oscillator [1, 2] is
                                                                 mentioned here under the category of momentum analysis
2.3 Applying a Moving Average Line                               [3] and not under trend analysis). The indicator instead
   In addition to trend analysis, momentum analysis is           assume there are no trends and always predicts that the
another important measurement of stock price data.               stock price will return towards the average. It therefore
Momentum analysis measures the rate of change in the             only takes advantage of very recent changes in stock price,
stock prices [3]. Some systems which use momentum                something which regression analysis is not as nimble with.
analysis as a primary means for judging which stocks to buy      This technique shall therefore be applied when designing
and sell use indicators such as Granville’s Law [4] and          the final system in the hopes that it will compensate for
Stochastic Oscillator indicator [2] as their expertise at        when regression analysis cannot find a good fit for the stock
predicting when to buy, sell, and hold a stock. These            price data, meaning there is too much fluctuation in price.
indicators [4,2] rely heavily upon comparing the current
stock price to a moving average line (MAL). The idea is
that when current stock price (MEL) moves above the              3    A Note on other Approaches
moving average line (MAL), then the current stock price is
                                                                   Before diving into the design of the system to solve the
overvalued and will likely fall, thereby indicating a good
                                                                 make-believe stock market problem, it is worth briefly
noting a few hybrid approaches and why they are                  shares: regression analysis [3], and a moving average lines.
unnecessary for solving the problem at hand.                     The set of rules created from applying these two systems
   One hybrid system uses genetic algorithms in                  will be tailored to return values between -10 and 10
conjunction with an expert system to select the good rules       (inclusive) [2] to indicate whether to sell or buy shares
using historical data [1]. Instead of manually tweaking the      respectively. Then, the antecedents of the final rule-set will
system’s underlying rule-base over time, all possible rules      depend on the values returned. These rules will decide
are available in a rule-base [1]. From this rule-base, subset    whether to buy, hold, or sell the stock.
rule-bases are selected and incorporated iteratively into
system [1]. Each new rule set is then analyzed for
                                                                 4.1 Using Regression Analysis as a Contributing
performance against the historical data [1]. Using this              Solution
evolutionary system, rule subsets are both created and
tested programmatically [1]. The advantage here is that               It seems reasonable to believe that predicting the next
                                                                 stock prices is as simple as finding a formula to fit the line
there is no ambiguity as to what which rules need to be
                                                                 connecting all of the daily points comprising the stock
added or removed to improve the performance. Using brute
                                                                 price, and then extrapolating the next value. Such a
force, the system continues test for a superior rule-subset.
                                                                 technique is called regression analysis and will be without a
   The above approach may be a bit radical in that each rule     doubt an incredibly powerful tool for predicting stock
is either accepted or rejected as being part of the system -     prices [3] in the case of the make-believe stock market
there is no middle ground.            An entirely different      where patterns are nested within the data.
genetic/rule-based hybrid approach assigned weights to
each rule denoting their importance [2, 5]. The resulting
weighted rule-set was referred to as an expert and were          4.1.1    Complications
generated using a genetic algorithm [2]. At runtime, the            Regression analysis, however, is not as simply applied as
system would consult various experts and judge each              it appears. When using high-order polynomial curves in
expert’s performance based on certain criteria [2]. Once an      regression analysis, the resulting formula tends to have a lot
expert best suited to the stocks available at the time was       of unnecessary curvature, making extrapolation particularly
selected, the expert was used to pick which stocks to buy        difficult. In figure 1, regression analysis is used to produce
and sell [2].                                                    a formula satisfying the three points falling on a line. The
   When genetic algorithms are hybridized with expert            result is a line that fits each of the three points very well,
systems, the goal is frequently to programmatically generate     but the values plummet towards negative infinity outside
sub-rule-sets and evaluate sub-set’s performance. The            beyond the range of the last value. In the case of the make-
advantage here is that the computer does all the number          believe stock market problem, a prediction of the stock
crunching rather than tweaking the rule base by hand. The        price after the third point using this mechanism would result
disadvantage (based on the previous two approaches) is that      in the system desperately wanting to sell when it should
these genetic systems do not manipulate the rules                clearly buy. This is a well documented phenomenon known
themselves in an intelligent way. If a specific rule is          as “Runge’s Phenomenon” [6]. And although there are
undervalued or uninformed, there is nothing in the system        techniques to mitigate it such as the Chebysheve’s Nodes
to improve the rule itself or create completely new ones.        and the use of spline curves [6], solving such complexities
The system can only improve its performance by weakening         reside outside the scope and the limitations of time placed
a rule’s importance or by removing it entirely.                  upon this project. Instead, different techniques for applying
   Systems such as these are useful when there are lots of       regression analysis will be used.
rules and the rules are for the most part independent of one
another. In the case of these two systems, the rules are
based on a large number of factors external to just the stock
price data. For smaller sets of rules such as that used in the
final design of the system discussed later, it may very well
be just as effective to tweak the rule-set by hand in order to
optimize it since manual adjustments will presumably be far
more intelligent.


4   The System Design
   The system that will be built to tackle the imaginary
stock market problem will use two primary techniques to
recognize good opportunities for buying and selling stock
                                                                   regression, then the parabolic test should not be performed
                                                                   because A. the pattern has already been determined and B.
                                                                   the data could not be properly extrapolated since the curve
                                                                   may plummet towards positive or negative infinity just
                                                                   beyond the end of the graph.
                                                                      Each of the most recent 50, 20, 10, and 5 regressions will
                                                                   each have a separate error factor associated with the fit for
                                                                   that particular number of points. The details concerning
                                                                   how this plays into whether or not to buy, sell, or hold a
                                                                   stock is once again dictated by the rule-set.


                                                                   4.2 Using the MAL as a Contributing Solution
                                                                        When regression analysis does not provide an adequate
                                                                   fit to the points comprising the stock price history, then
                                                                   rules will be used that incorporate the use of a moving
     Figure 1. Using high-order polynomials to represent
                                                                   average line. In the design of this particular system, the
                    three linear points.                           Stochastic Oscillator indicator will be used to forecast
                                                                   whether to buy, sell, or hold a stock just as they have been
                                                                   in prior rule-based expert systems [2].
4.1.2   Using Linear and Hyperbolic Regression                          Since the both the math driving this indicator and the
     Analysis                                                      details of its application in other environments lie beyond
   One way of circumventing Runge’s Phenomenon is to               the scope of this document, the summary of its workings
simply avoid the production of higher level degree                 expressed here will be brief. Like the application of
polynomial functions when using regression analysis. If a          Granville’s law [4], the Stochastic Oscillator indicator [6]
linear regression technique were used instead of a                 uses moving averages to compute what to do with a stock.
polynomial regression, then the fit would be flawless, rather      The comparison is done using two oscillators, namely a fast
than being close to flawless. However, points falling on a         and a slow oscillator [6]. The independent variable of the
perfect line should be considered a rare event – especially        fast oscillator is computed using the following formula:
when the number of points is large. The far more likely            (Today’s price – Low)/(High – Low); where Today’s price
                                                                   is the current price of the stock, the Low is the lowest price
circumstance would be when the linear regression analysis
                                                                   over a defined time period (usually two weeks) and the
yields a poor fitting line for the data. For example, it
                                                                   High is the highest price over the time period [6]. The
should be expected that if the graph of the stock data
                                                                   resulting dependent variable is usually called K [6]. The
happens to take the form of a bell curve, it will not fill well    slow oscillator is where the moving average is factored into
to line. In such a case, the expert system’s rules will likely     account [6]. The slow oscillator’s dependant variable is
reject the data, which is why a variety of fits will be            computed by using the moving average the value of the fast
attempted by the system and their acceptance will be               oscillator over the past few days (which is usually three)
quantified by the expert system’s rules.                           [6]. The computed dependent variable here is usually
   Since it is highly unlikely that linear regression analysis     called D [6]. The buy action is trigger when K crosses
will produce a flawlessly fitting line, other regression           up/beyond/through D. The sell action is triggered when K
analyses will be used as well. In addition to fitting all of       crosses down/past/through D [6]. Pseudo rules will
the points for a stock, the system will additionally test the      therefore reflect the following spirit [7]:
most recent 50, 20, 10, and 5 points (when applicable) for
the stock. The significance of these tests will be dictated by
                                                                       If K is smaller than D then sell
the rule-base, which will be explained in more detail in a
later section.                                                         If K is larger than D then buy
   Since linear regression analysis will only work well when           If K and D are small, then buy
the data falls more or less on a line, the system will also test       If K and D are large, then sell
for a fit when points fall more or less on a parabola (y =
Ax^0 + Bx^1 + Cx^2). Once again, in addition to fitting all
of the points for a stock, the system will additionally test for       Once again, this mechanism should help take
the most recent 50, 20, 10, and 5 points for the stock. Once       advantage of daily fluctuations which the regression
again, the significance of the results will be judged by the       analysis would consider to be too erroneous to be put to
rule-base. Note that if there is a perfect fit for the linear      good use.
                                                                          K
                                                                          K
4.3 Applying the Rules
                                                                     Where (comparison_op) can be any one of the
     It is usually clear when certain rules should signal to         following values:
buy, and when certain rules should signal to sell. However,
such rules should take into account the degree of how good                <
a sell or buy is so as to quantify the amount that should be              >
bought or sold. This why nearly all such rules in the system         Where (LVL) is can be as follows:
will return values between -1 and 1 (inclusive) where -1
means buy¸0 means hold, and 1 means sell [2].                             A value ranging from -1 to 1 inclusive.
                                                                          K
                                                                          D
4.3.1    Regression Analysis Rules
     In the case of regression analysis, the confidence in the
fit (100% - Error%) will be multiplied by the predicted          4.3.3    Applying the System’s Rules
percent loss or gain for the following day. This will yield a         For each stock, the system will attempt to execute each
product denoting the goodness of the overall fit. This value     rule in the database. For each tested stock, a single average
will also be scaled to the [-1, 1] system. Rules representing    value between -1 and 1 (inclusive) denoting the general
regression analysis will therefore be expressed in the           goodness of the stock will be stored into the system’s
following format:                                                memory. Once all of the stocks have been processed, the
                                                                 stocks will be sorted according to their goodness value [3].
    if (FIT)(comparison_op)(LVL) then (LVL)                      Those stocks already owned with the lowest values that
                                                                 surpass a certain hardcoded threshold will be sold and those
                                                                 stocks with the highest goodness value beyond a certain
    Where (FIT) can be any one of the following values:          threshold will be purchased to replace them [3]. The word
         50_DAY_LINEAR_FIT                                       replace is used here because the system will naturally want
         20_DAY_ LINEAR_FIT                                      to avoid unnecessary
         10_DAY_ LINEAR_FIT
                                                                 5   Concluding Remarks
         5_DAY_ LINEAR_FIT
                                                                      Most research that has been done using expert systems
         50_DAY_PARABOLIC_FIT
                                                                 to solve the stock market problem has done so using lots of
         20_DAY_ PARABOLIC_FIT                                   rules acquired from many different indicators. These
         10_DAY_ PARABOLIC_FIT                                   indicators do not rely exclusively on the stock price and so
                                                                 oftentimes require complex hybrid systems to gather and
         5_DAY_ PARABOLIC_FIT
                                                                 decipher the vast amounts of information available to help
    Where (comparison_op) can be any one of the                  make a smart decision regarding stock trades. The make-
    following values:                                            believe stock market problem presented here is therefore a
         <                                                       very interesting version of the real stock market, where real
                                                                 trades can and should be based on stock-price data alone.
         >                                                       Although the system has not been built yet, since the system
    Where (LVL) is a value ranging from -1 to 1 inclusive.       incorporates both trend analysis via regression analysis and
                                                                 momentum analysis [1] via the Stochastic Oscillator
                                                                 indicator [1, 2, 6], it should perform well given the
                                                                 particular data it has been provided with to make its
                                                                 decision whether to buy, sell, or hold stock in the make-
                                                                 believe stock market.
                                                                     transactions and so keep only a few stocks at any one
                                                                 point in time.
4.3.2    Stochastic Oscillator Rules


    if (KD)(comparison_op)(LVL) then (LVL)

    Where (KD) can be any one of the following values:
       K_AND_D
                                                          3. Conger., S., and Loch, K.D. (eds.). Ethics and computer
                                                             use. Commun. ACM 38, 12 (entire issue).
                                                          4. Mackay, W.E. Ethics, lies and videotape, in
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1. Anderson, R.E. Social impacts of computing: Codes of      Press, 138-145.
   professional ethics. Social Science Computing Review
                                                          5. Schwartz, M., and Task Force on Bias-Free Language.
   10, 2 (Winter 1992), 453-469.
                                                             Guidelines for Bias-Free Writing. Indiana University
2. CHI Conference Publications Format. Available at          Press, Bloomington IN, 1995.
   http://www.acm.org/sigchi/chipubform/.

				
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