these indicators provide into a useful model. This is accomplished automatically by the Statistical Network.

The technical indicators, their abbreviation, and a brief description are listed in Table 17.1. Many of these indicators require specification of a time window, and may therefore result in many different actual input variables depending on the time windows selected. In these cases, the set of time windows for each are also listed, and are designated by an "XX" in the variable abbreviation (e.g., ExponMWA XX where XX = 30 is the 30-day Exponential Moving Window Average). This results in a set of 86 input variables for our problem.

Table 17.1 Contd.

Indicator Name Abbreviation Time Windows

Description

The difference of two moving averages of the price of a security.

Price Rate-Of-Change PriceRateChangeXX 5, 10, 15, 20, 30, 45, 90

Description

The difference in current price and the price XX time periods ago, expressed in percent. Price and Volume Trend Price Vol umeTrend None

Description

A cumulative total of volume, weighted by changes in closing price.

TRIX TRIX-XX 5,9,12,14,20,21,26,30,45,90

Description

A momentum indicator involving a triple exponential average.

Typical Price TypicalPrice None

Description

An average of the High, Low, and Close of each days price.

Vertical Horizontal Filter VerticalHorizontalFilterXX 28

Description

Indicates whether prices are trending or congested.

Volume Oscillator VolumeOscXXl-XX2 3/10,3/15, 5/10, 10/20, 10/30,

10/45, 30/90

Description

The difference between two moving averages of a securitys volume.

Volume Rate-Of-Change VolumeRateChangeXX 5, 10, 15, 20, 30, 45, 90

Description

The difference in current price and the price XX time periods ago, expressed in percent. Williams %R WilliamsR-XX 5, 10, 15, 20, 30, 45, 90

Description

A momentum indicator measuring overbought/oversold conditions.

A variety of technical indicators were used as input variables to model Buy/Sell conditions.

Performance Target Selection

To define the Buy and Sell indicators, it was necessary to choose "performances targets." Ideally, we want the Buy/Sell indicators to tell us when the value of a particular stock will change more than predefined thresholds; that is, when it will rise a certain percentage or more and when it will fall another certain percentage or less. These performance targets form the basis of our Buy/Sell indicators.

We chose an annual gain of 35 percent and an annual loss of-15 percent as our performance targets. These were scaled to the time periods shown in Table 17.2. The goal is to select the best time period yielding the most accurate Buy/Sell Indicators. Note that other performance targets may be used, and with potentially better results than reported here.

To produce the actual Buy/Sell indicators, we first calculated the percentage gain or loss over the time periods indicated of the stocks closing price. We then determined whether these percentages exceeded the Gain/Loss thresholds listed in Table 17.2. If so, a value of "1" was assigned to the indicator, else a value of "0" was assigned.

Selection of Predictive Time Period

Four subsets of the data ( , , C, and D) each containing approximately 4,000 observations were selected at random from the entire set of approximately 72,000 data. For each of the 10 Buy/Sell indicators (i.e., 5 Buy indicators and 5 Sell indicators), two Statistical Networks were synthesized using subsets A and B, for a total of 20 networks. Testing was performed on subsets and D. Table 17.3 shows the performance of each Statistical Network model, ranked by Average Absolute Error.

Here, it is obvious that longer periods produce better results. Therefore, the remainder of our modeling was performed using time periods of 90 days and the corresponding Buy/Sell indicators. Note that the networks ideally output values of "0" and "1." The average errors of these networks range from 0.34 to 0.48; in all cases this is better than "guessing," which has an average error of 0.5-

Several time periods were chosen, each with an annual gain of35 percent and an annual loss of-15 percent.

Table 17.3 Performance of initial buy/sell indicator networks

Longer time periods showed a clear superiority for indicating buy and sell conditions.

Information Content Analysis

Typically, for large input sets such as that used here, it is useful to reduce the number of inputs considered to allow better focus on the input variables used. A particularly useful method for this is Information Content Analysis™}1 Here, we take advantage of the fact that Statistical Networks synthesized at higher values of CPM are more "discriminating" and will therefore retain only the input variables that contain a high information content.

The information content of a set of input variables is quantified by synthesizing a set of Statistical Networks over a range of CPM values, and weighting the frequency of occurrence of each input over the set of networks to emphasize the inputs retained at higher CPM values. The key advantage to the ICA is that not only will useful input variables be identified, but also valuable combinations of inputs, because Statistical Network nodes can mathematically combine two or three inputs.

We performed an ICA for each of the four data subsets described for both the 90-day Buy and 90-day Sell indicators, and averaged the results. Typically, most of the input variables will have a zero information content-they will not appear in any of the synthesized networks. Table 17.4 shows the normalized information content of each technical indicator for both Buy/Sell indicators. Only input variables with an information content greater than 0.100 were used for subsequent modeling. Also, only a subset of all input variables has non-zero information content.

Baseline Models

To produce a set of baseline results, four subsets of the data (E, F, G, and H), each containing approximately 16,000 observations, were selected at random from the entire set of data. For the two Buy/Sell indicators, a Statistical Network was