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Before outlining the procedures of decision rule modeling and presenting a practical example, look at some potential applications. In economics, identification of a consistent pattern of changes in the leading and lagging economic indicators could be used to provide a decision rule definition of the peaks and troughs in the business cycle which might be both more timely and consistent than the proclamations of a committee. A decision rule model might be well suited to the monetary analyst in assessing the weekly Condition Statement of the Federal Reserve Banks and other data in determining whether the Fed has really "loosened" or "tightened" its policies concerning the rate of expansion of money and credit. The industry or company analyst could examine the relevance of changes in the industry statistics or in the balance sheets and income statements of companies in the industry to the price of shares of those companies. Similarly, the usefulness of trading rules of the "technical" analyst can be tested for relevance.

Finally, a strong case can be made for developing and using your own decision rules for investment purposes for two reasons. First, when you develop rules yourself, you will have more confidence in them and will be more likely to use them than you would be inclined to act on someone else's advice. Secondly, when an advisor is so well publicized that too many people are acting on his advice, the system can become ineffective due to its own success. The trade-off here is that developing decision rules, even with computers, is hard work and very time consuming. In this article, a demonstration study of a set of decision rules for trading the gold market will be provided.

In conducting a pattern recognition research study, there are six phases which are generally common to all types of mathematical modeling:

1. formulating the problem
2. collecting or mathematically creating the data series to be used in identifying and indicating the patterns to be studied
3. developing decision rules which will identify the initiation of patterns from the indicator series
4. testing the decision rules and evaluating the predictive results in the forecast series
5. establishing control over the use of the decision rule, and
6. proceeding to implement the actual use of the decision rules.

Each of these phases generally consist of several steps which are subject to frequent re-evaluation and re-working as a study progresses.

Formulation of the problem

The first phase consists of defining the subject of the study and how it is to be conducted. In the example study, the objective was to find an "acceptable" set of decision rules for trading gold. Acceptable decision rules are defined as participating in as many long and short trading opportunities as possible with a profit potential in excess of that which could be earned while investing in the money market over the same period. These rules should make profits in more than one-half of the trades so that the overall return would significantly exceed the return available by simply investing in the money market. The test period chosen was 1861 through 1985, a period of 125 years.

In order to attain this objective, the study will analyze the smoothed difference between a fast and a slow smoothed series of the price of gold itself. Smoothed series can be obtained in a number of ways, such as moving averages, moving least square linear fitting, and exponential smoothing. A fast smoothed series gives more weight to recent prices, while a slow series places more weight on older prices (for instance, a 5-period moving average is faster than a 40-period moving average). In the demonstration study presented in this article, the fast series is a single exponentially smoothed series (column 3) with a factor of 0.142857 (approximately a 13-week moving average), and the slow series is a single exponentially smoothed series (column 4) with a factor of 0.074074 (26-week moving average).

"Empirical modeling simply tests the statistical relevance of qualitative correspondence between observed events. "