# Neural Networks and Genetic Algorithms: Another Tool For The Technical Analysis of Financial Markets. Donn S. Fishbein, MD, PhD

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2 signaled under the opposite conditions. If SMAs of different lengths are plotted together, a buy is signaled when the shorter length SMA crosses above the longer length SMA. Using these rules and referring to Chart 1, a sell is clearly indicated in February, 2001, with no subsequent buy indicated. Note that the 10 day and 50 day SMAs converge in February, 2002 only because the stock simply can t go any lower. The greatest weakness of SMAs is that they tend to arrive late to the dance (suffer from lag.) A part or the entirety of a market move may have already occurred before a SMA signals a buy or sell. This is most pronounced in a market with no major trend, where reliance on SMAs alone can lead to a long succession of small losing trades. In the worst case, when a SMA has a period equal to half of the period of a market instrument with a regular period, the signals are 180 degrees out of phase, and every trade signaled is a loser. In an attempt to address weaknesses in the fixed period SMA, numerous variations have been developed. Two main strategies are to vary the weighting of individual prices, usually giving more weight to more recent prices, or to vary the period over which the average is calculated, either in a static or dynamic fashion. The exponential moving average (EMA) is expressed as the sum of a percentage of the previous period s EMA and a percentage of the current period s value. The effect is to deemphasize older data and more heavily weight current data. The relative weights determine the effective length of the EMA. Another approach is to change the length of the moving average based on the underlying data it is calculated upon. The calculated period may be fixed or vary from period to period. The TRIX (TRIple exponential moving average) is derived from the EMA, and is defined as the percentage rate of change of an EMA of an EMA of an EMA of the underlying price. The TRIX provides a smoothed version of the price, which can then be used in a number of ways. Chart 2 shows a daily price chart for the S&P 500 market index, along with a TRIX indicator. TRIX is an unbounded oscillator that varies about the zero line. Its simplest interpretation is that a zero crossing to the upside is a buy indicator, and a zero crossing to the downside a sell indicator. This simple interpretation yields only modest results, 2

3 with an annualized yield of just 3.6%. Chart 3 shows the trades (up arrow buy, down arrow sell) generated by this system over a five year period. One of the difficulties in using this indicator is that there are a number of parameters to choose, namely the length of each of the three EMAs and the period over which the percentage change is calculated. One can rely on standard parameters (usually 9 or 12 periods) for each EMA, or determine them on a case-by-case basis. Then there is the problem of how to employ this indicator to generate buy and sell signals. The application of neural networks and genetic algorithms (NNGA) can help with this task. Neural networks (NN) can assist in finding a relationship, or mapping, between inputs (price, TRIX) and an output (price sometime in the future.) Genetic algorithms (GA) can assist in the optimization of this relationship, particularly in selecting the optimal parameters for each EMA and the percent change indicator. A basic introduction to artificial neural networks, genetic algorithms, and technical analysis can be found in an earlier paper (Fishbein, DS. Trading Financial Markets With Neural Networks and Genetic Algorithms, TCF Proceedings 2001), as well as in many other locations (see reference list). The following discussion will explore various interpretations of the TRIX indicator as applied to trading instruments based on the Standard and Poor s 500 Index (S&P 500, SPX), along with the integration of several other market indices as potential NN inputs. In the first implementation, a GA is used to select the optimal parameters for the TRIX indicator, and a training process is used to develop weights for the interconnections within a NN that map the input, the value of TRIX, to the output, the predicted opening value two days after the closing value. This predicted value is then used to signal buys and sells. Selling in this case refers to selling the index short, not simply closing the long position. The trades can be executed by either trading the SPDR (S&P 500 Depository receipts), or S&P 500 futures. The network is trained over a four year period, from the second quarter of 1996 to the first quarter of During the training period, the network showed an annualized return of 32.1%, more than double the return on a buyand-hold strategy during the same period. One danger with neural networks is that the network doesn t learn anything or develop the ability to generalize, but simply memorizes its input/output pairs. While a 3

6 networks remain profitable. Boise Cascade, whose market profile is more similar to the S&P 500 index, performs more consistently across the five systems than does the Nasdaq 100 index, particularly within the evaluation period. These findings give further confidence in the validity of these network designs. Selection of inputs more related to the underlying fundamentals of the Nasdaq 100 market could probably improve on results in that market. Conclusion The recent Enron debacle has served to highlight the shortcomings of traditional fundamental analysis of stocks as performed by most Wall Street analysts. Technical analysis can provide a methodical, emotionless approach to trading financial markets. The use of neural networks and genetic algorithms improves on traditional technical analytic techniques. Networks of fairly simple design can achieve quite satisfactory results. References Acheli, Steven B. Technical Analysis from A to Z. Fosback, Norman G. Stock Market Logic. Dearborn Financial Publishing, Inc., Zirilli, Joseph S. Financial Prediction Using Neural Networks. International Thomson Computer Press, Zweig, Martin. Winning On Wall Street. Warner Books,

7 TABLE 1 Market/ Network Training, Annualized Return % Evaluation, Annualized Return (%) S&P 500 Index TRIX NO OPT 3.6 n/a TRIX OPT TRIX OHLC OHLC VIX ADV OHLC VIX ADV 6 walk Boise Cascade Corp TRIX NO OPT -8.4 n/a TRIX OPT TRIX OHLC OHLC VIX ADV OHLC VIX ADV 6 walk Nasdaq 100 Index TRIX NO OPT 12.7 n/a TRIX OPT TRIX OHLC OHLC VIX ADV OHLC VIX ADV 6 walk

8 CHARTS Chart 1 Enron and 3 Simple Moving Averages Chart 2 SPX and TRIX 8

9 TRIX NO OPT Chart 3 Trading the SPX with the unoptimized TRIX indicator TRIX Apr Jul Oct Jan 2002 Chart 4 Trading the SPX with an optimized TRIX indicator 9

10 OHLC TRIX Oct Nov Dec Jan 2002 Feb Mar Chart 5 Trading the SPX with an OHLC and TRIX network OHLC VIX ADV Oct Nov Dec Jan 2002 Feb Mar Chart 6 Trading the SPX with an OHLC, VIX and ADV network 10

11 6 Walk OHLC VIX ADV Apr Jul Oct Jan 2002 Chart 7 OHLC, VIX, ADV network, 6 walk-forward periods 11

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