For this experiment, we decided to include three basic patterns in the final system: pull-backs-in-trends, multiple bottoms and tops, and head-and-shoulders patterns. We considered both the long (upward) and short (downward) varieties of each pattern, which yielded six patterns in total.

A "pull-back-in-trend" is a situation in which a trend in the movement of the market has clearly been established, but the market reverses for a short time before continuing in the direction of the trend. The key is to jump in at the extreme of the pull-back. There may be several pull-backs along the way to a major top or bottom. As such, pull-backs-in-trends provide favorable entry points in the direction of the overall trend. On the long side of this pattern, there were 194 marks; 140 instances were identified for the shorts.

The "multiple bottoms and tops" pattern occurs when there are clear-cut bottoms or tops that are pull-backs in trends, with an emphasis on double- or triple-bottoms or tops. No definite trend has to be present for this pattern to occur; in fact, we are looking for the end of a major trend or where there is no trend, as in market consolidation periods, to differentiate the multiple bottoms and tops pattern from a pull-back in trend pattern. There were 150 instances for the longs, 145 for the shorts.

The "head-and-shoulders" pattern is when the market forms a sort of hump (a rise followed by a decline), pulls back a bit, forms a higher hump (usually with some noise in it), pulls back again, and finally forms another smaller hump (relative to the second one), at which point the market drops off. When marking this pattern, we would click on the chart a little after the peak of the rightmost hump, which would indicate a good place to sell. There were fewer markings for this pattern than for the multiple bottoms or tops pattern: only 48 on the long side, 19 on the short.

We used our neural network development tool, N-TRAIN®, to train one neural network for each of the six patterns. All six nets had the same structure: 25 inputs in the first layer, 6 middle layer cells, 1 output. The output was what we wanted the network to predict-whether or not the chart pattern was present. They were essentially simple, unadjusted networks; in fact, the networks were trained using mostly default settings of N-TRAIN®.

All the networks had the same parameters. In all cases, the inputs to the networks were the same. Input data is examined by the networks to determine whether a pattern is present. While, we cannot fully disclose the precise nature of the input signals because of their proprietary nature, we can say that they consisted of the slopes of several moving averages of different periods (for trend information), as well as specially normalized price change values.

The data sample used for this study consisted of the period from 1/3/83 through 5/3/96; there are 3,322 bars in this sample. Bars 10 through 2,599 were used to train all six networks; bars 2,600 through 3,322 were used as the out-of-sample test data for all six systems.

The neural networks were all trained until correlations between their output and the target had reached a plateau with the in-sample data set. This usually occurred by 200 training runs for each network. After each net was trained, it was then

"polished" with a very small learning rate for about 20 runs. Training for the in-sample runs ranged between 0.20 and 0.60; in the out-of-sample runs, they ranged between 0.08 and 0.50. In most cases, there was reasonably good generalization.

After the networks were trained and tested, we entered TradeStation® and wrote the trading rules for each of the six networks, which constituted six systems. The entry rule for all six systems was the same, with the exception of a threshold parameter, which varied somewhat from net to net. Thresholds were adjusted for each system to get a reasonable number of trades from each system. As it turned out, the threshold was not too critical for most of the patterns: If it was too low, there would be more signals than would be expected based on the marking procedure and the profits would drop; if the threshold was set too high, it would not necessarily hurt individual trade performance, there would just be fewer trades (e.g., there might be 100% wins, but only with 10 trades). We, therefore, set the thresholds to a middle range, a value that would provide a number of trades roughly equal to the number of instances of the pattern we had marked on the chart, and would also provide an acceptable profit.

The entry rule was "If the networks output is greater than the threshold, then buy/sell next bar." The exit rule was based on a proprietary, "quasi-parabolic" ratcheting stop: Basically, the stop would start out (for the long side) some multiple of the average range below the entry price, and it would go up with the market, becoming like a moving average pulling toward the market as the market rose; in this way, the stop would rise along with the market to lock in profits. Aside from the threshold parameter, the stop acceleration was the only factor that varied across the systems (in a couple of the short patterns, we needed to alter the acceleration factor to prevent market volatility from causing stops to be hit too quickly).

We combined the six systems into one integrated system. We ran the integrated system with a money management stop of $7,500, and a profit target of $2,000. A money management stop is designed to exit a trading position when the trades net loss exceeds a specified amount, in this case $7,500. A profit target is designed to lock in profits by exiting the trade as soon as the trades net profit reaches a specified amount, in this case $2,000.

A Note about the Figures and Tables

The charts are standard bar charts, with opens and closes marked for each bar. Several kinds of signals are generated by the systems on the out-of-sample data, which extended from 2/26/93 to 5/3/96:

• An arrow pointing upward with a 1 indicates a long entry signal.

• An arrow with a -1, pointing downward, indicates a short entry signal.

• An arrow with a 0 and a horizontal bar at the top or at the bottom indicates an exit from the trade.

"polished" with a very small learning rate for about 20 runs. Training for the in-sample runs ranged between 0.20 and 0.60; in the out-of-sample runs, they ranged between 0.08 and 0.50. In most cases, there was reasonably good generalization.

After the networks were trained and tested, we entered TradeStation® and wrote the trading rules for each of the six networks, which constituted six systems. The entry rule for all six systems was the same, with the exception of a threshold parameter, which varied somewhat from net to net. Thresholds were adjusted for each system to get a reasonable number of trades from each system. As it turned out, the threshold was not too critical for most of the patterns: If it was too low, there would be more signals than would be expected based on the marking procedure and the profits would drop; if the threshold was set too high, it would not necessarily hurt individual trade performance, there would just be fewer trades (e.g., there might be 100% wins, but only with 10 trades). We, therefore, set the thresholds to a middle range, a value that would provide a number of trades roughly equal to the number of instances of the pattern we had marked on the chart, and would also provide an acceptable profit.

The entry rule was "If the networks output is greater than the threshold, then buy/sell next bar." The exit rule was based on a proprietary, "quasi-parabolic" ratcheting stop: Basically, the stop would start out (for the long side) some multiple of the average range below the entry price, and it would go up with the market, becoming like a moving average pulling toward the market as the market rose; in this way, the stop would rise along with the market to lock in profits. Aside from the threshold parameter, the stop acceleration was the only factor that varied across the systems (in a couple of the short patterns, we needed to alter the acceleration factor to prevent market volatility from causing stops to be hit too quickly).

We combined the six systems into one integrated system. We ran the integrated system with a money management stop of $7,500, and a profit target of $2,000. A money management stop is designed to exit a trading position when the trades net loss exceeds a specified amount, in this case $7,500. A profit target is designed to lock in profits by exiting the trade as soon as the trades net profit reaches a specified amount, in this case $2,000.

A NOTE ABOUT THE FIGURES AND TABLES

The charts are standard bar charts, with opens and closes marked for each bar. Several kinds of signals are generated by the systems on the out-of-sample data, which extended from 2/26/93 to 5/3/96:

• An arrow pointing upward with a 1 indicates a long entry signal.

• An arrow with a - 1, pointing downward, indicates a short entry signal.

• An arrow with a 0 and a horizontal bar at the top or at the bottom indicates an exit from the trade.