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Prediction the stock market with genetic programming

D
David Moskowitz, Ph.D.

The document discusses using genetic programming to predict stock market movements. It provides an overview of genetic programming, describes how it has been applied to problems like time series prediction and stock market prediction, and discusses the author's experiments applying genetic programming to predict the S&P 500 index. The results show that in some periods, genetic programming outperformed traditional models and the buy and hold benchmark strategy in terms of investment gains, particularly when transaction costs were not considered.

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Predicting the Stock Market with Genetic Programming David Moskowitz, Ph.D. Infoblazer LLC Data Scientists in Stamford Westport January 25, 2016
Disclaimer • The following is my opinion only • It is not the opinion of my employer • It is not related to any work done at my employer You should not make any decision, financial, investments, trading or otherwise, based on any of the information presented without undertaking independent due diligence and consultation with a professional broker or competent financial advisor. You understand that you are using any and all information presented at your own risk.
Agenda • What is Genetic Programming? • Time Series Prediction • Stock Market Prediction • Other Issues • Modularity • Linear GP • Genetic Algorithms • Demonstrations
What is Genetic Programming? • Get a computer to do something without telling it how to do it • Breeds a population of computer programs that improve over time • Evolution • Genetic Operators • Survival of the Fittest • Stochastic component • Non-Greedy • Creativity • Novel solutions • Size and shape of solution unknown • Limited only by what can be represented as a computer program (Koza et al., 2006, p. 11)
Example: Design of a Satellite Boom • Designed using a genetic algorithm • 20,000+% improvement in frequency averaged energy levels (Keane, 1996)
History • Visionaries • Samuel 1959 – Goal of AI • Turing 1948 – Evolutionary search, gene combination, survival of the fittest • Evolutionary Algorithms , 1962- • mutation , populations, • Genetic Algorithms, 1973- • John Holland • Crossover • Genetic Programming, 1989- • John Koza • Best way to represent a computer program is a computer program
How GP Works • Preparatory Steps • Primitives • Fitness Function(s) • Initialize Population • Evolve Population • Calculate population fitness • Select next generation • Termination Condition (Poli et al.,2008, p. 2)
GP Representation • LISP • (max (+ x x) (+ x (* 3 y))) • max(x+x,x+3*y) MAX X + + *X X 3 y
GP Operations • Probabilistically select an operation • Crossover • Switch two nodes on different individuals • Mutation • Randomly modify an individual (node) • Reproduction • Copy parent, as is, to next generation
GP Selection • Need to select one or two individuals for genetic operations • Selection is probabilistic • Fitness Proportional Selection • Tournament Selection
Crossover + + X y 3 * + y 1 / X 2 + + X y 3 * + y 1 / X 2 Parents Children
Mutation * + y 1 / X 2 Parent Child * + y 1 * 2 MIN X y
Demo – Symbolic Regression • Curve Fitting • 𝑥3 − 𝑥2 + 𝑥 − 4 • Prove that GP works -200000 0 200000 400000 600000 800000 1000000 1200000 0 10 20 30 40 50 60 70 80 90 Y X Demo a, b
Chaotic Series • Look random, but are deterministic • Highly dependent on initial conditions • Difficult to predict 𝑌𝑡 = 𝑠𝑖𝑛 𝑥 − 130 + 𝑥 + 130 x=0: 𝑌0 = 0.9 X>0: 𝑌 𝑡+1 = 4𝑌𝑡(1 − 𝑌𝑡) 0 0.2 0.4 0.6 0.8 1 1.2 0 10 20 30 40 50 60 70 80 90 Y X 9 10 11 12 13 14 15 16 17 0 10 20 30 40 50 60 70 80 90 Y X
Demo- Chaotic Series Symbolic Regression Demo c, d, e, f
Regime Change • Goal is to uncover underlying data generating process • This can change over time -15 -10 -5 0 5 10 0 14 28 42 56 70 84 98 112 126 140 154 168 182 196 Y X 0<=x<70: 𝑌𝑡 = 𝑠𝑖𝑛 𝑥 + 𝑥 70<=x<130: 𝑌𝑡 = 𝑐𝑜𝑠 𝑥 − 𝑥 130<=x<200: 𝑌𝑡 = 𝑠𝑖𝑛 𝑥 − 130 + 𝑥 − 130 -3 -2 -1 0 1 2 3 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Y X x<200, x>=300: 𝑌 𝑡+1 = 4𝑌𝑡(1 − 𝑌𝑡) 200<=x<300: 𝑌 𝑡+1 = 1.8708𝑌𝑡 − 𝑌𝑡−1 S&P 500 index close price during the stock market crash of 2008 (Yahoo, 2013). 𝑌𝑡 = 𝑓 𝑊𝑇𝐹 ?
Demo- Symbolic Regression Regime Change Demo g
Time Series Prediction • Train on past values • Predict future values • Retrain periodically
Demo- Chaotic Series Prediction Demo h, I, j
Market Prediction • S&P 500 Long-Flat (Invest-don’t invest) • Ignore transaction costs • Ignore out of market returns • Predictors • S&P 500 Price • S&P 500 Volume • 250-day MA normalized 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 500 1000 1500 2000 2500 S&P 500 Index Series Index Value 250 Day Moving Average 250-day MA Normalized
GP is a Perfect Match for Market Prediction • “The interrelationships among the relevant variables is unknown or poorly understood (or where it is suspected that the current understanding may possibly be wrong).” • “Finding the size and shape of the ultimate solution is a major part of the problem.” • “Significant amounts of test data are available in computer-readable form.” • “There are good simulators to test the performance of tentative solutions to a problem, but poor methods to directly obtain good solutions.” • “Conventional mathematical analysis does not, or cannot, provide analytic solutions” • “An approximate solution is acceptable (or is the only result that is ever likely to be obtained)” • “Small improvements in performance are routinely measured (or easily measurable) and highly prized.” (Poli et al.,2008, pp. 111-113)
Primitive Set • Hundreds of indicators • Ex. (http://www.investopedia.com/active-trading/technical-indicators/) • Include common technical analysis indicators • Momentum- compare to recent average • Breakout- compare to recent minimum/maximum • Ex. Buy if current price risen by 2% over minimum price last 30 days • Prefer low level functions • Better results possible with higher level , packaged indicators?
Primitive set • Functions • Add • Subtract • Multiply • Divide • Gt • Lt • And • Or • Not • offsetValue • ifElseBoolean • movingAverage • periodMaximum • periodMinimum • AbsoluteDifference • Terminals • randomInteger(low high) • randomDouble(low high) • True • False • offsetValue(0) • Hundreds of other technical indicators (http://www.investopedia.com/active- trading/technical-indicators/)
Training Approaches • Train-Predict-Retrain • Train-Test-Predict • Multiple Runs Train M Test N Predict 1 Train Predict M N (1) Demo k, l, m
Experiment- Market Prediction • Investment decisions in S&P 500 Index • Modeled after (Chen et al., 2008), 1988-2004 • Long-Flat decisions • Normalized by 250-day moving average • Fitness = investment gain 0 200 400 600 800 1000 1200 1400 1600 1988-01-04 1988-08-16 1989-03-31 1989-11-10 1990-06-27 1991-02-08 1991-09-24 1992-05-07 1992-12-18 1993-08-04 1994-03-17 1994-10-31 1995-06-15 1996-01-29 1996-09-11 1997-04-25 1997-12-08 1998-07-24 1999-03-10 1999-10-21 2000-06-06 2001-01-19 2001-09-04 2002-04-25 2002-12-06 2003-07-24 2004-03-09 2004-10-21 2005-06-07 S&P 500 0.7 0.8 0.9 1 1.1 1.2 1.3 1988-12-27 1989-08-10 1990-03-26 1990-11-06 1991-06-21 1992-02-04 1992-09-17 1993-05-03 1993-12-14 1994-07-29 1995-03-14 1995-10-25 1996-06-10 1997-01-22 1997-09-05 1998-04-22 1998-12-03 1999-07-21 2000-03-03 2000-10-16 2001-06-01 2002-01-22 2002-09-05 2003-04-22 2003-12-03 2004-07-21 2005-03-04 2005-10-17 2006-06-02 Normalized
Experiment- Market Prediction • Training-validation-prediction approach (T-V-P) • Training-prediction approach (T-P) • Training - 1989-1998 • Prediction- 1999-2004 (Chen et al., 2008, p. 110)
Results T-V-P w/Trans Cost Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0751 GP 0.0434 0.0664 -0.1917 0.1197 [0.0250 ... 0.0618] 5/50 ADF 0.0309 0.0798 -0.3054 0.0845 [0.0088 ... 0.0530] 3/50 ADT 0.0510 0.0519 -0.1974 0.1042 [0.0366 ... 0.0654] 5/50 2001-2002 Buy & Hold -0.3144 GP -0.3693 0.1306 -0.8087 -0.2885 [-0.4055 ... -0.3331] 1/50 ADF -0.3347 0.0887 -0.7290 -0.1777 [-0.3593 ... -0.3102] 2/50 ADT -0.3697 0.1390 -0.7450 -0.0134 [-0.4082 ... -0.3312] 1/50 2003-2004 Buy & Hold 0.3332 GP 0.2945 0.0497 0.1432 0.3291 [0.2807 ... 0.3083] 0/50 ADF 0.3139 0.0390 0.1170 0.3539 [0.3031 ... 0.3247] 1/50 ADT 0.3247 0.0150 0.2349 0.3522 [0.3205 ... 0.3289] 2/50 (Moskowitz, 2016, p. 119)
Results T-V-P wo/Trans Cost Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0751 GP 0.1494 0.1088 -0.0438 0.4525 [0.1192 ... 0.1795] 35/50 ADF 0.1418 0.1238 -0.0399 0.5112 [0.1075 ... 0.1761] 35/50 ADT 0.1567 0.1099 -0.0068 0.4796 [0.1262 ... 0.1871] 37/50 2001-2002 Buy & Hold -0.3144 GP -0.3121 0.0573 -0.4081 -0.0348 [-0.3280 ... -0.2962] 17/50 ADF -0.3023 0.0848 -0.5153 0.0196 [-0.3258 ... -0.2788] 18/50 ADT -0.2843 0.0635 -0.3924 -0.1245 [-0.3020 ... -0.2667] 32/50 2003-2004 Buy & Hold 0.3332 GP 0.3045 0.0929 0.0463 0.5045 [0.2788 ... 0.3303] 15/50 ADF 0.3395 0.1171 -0.0016 0.5597 [0.3070 ... 0.3719] 22/50 ADT 0.3329 0.1202 0.0775 0.6443 [0.2996 ... 0.3663] 29/50 (Moskowitz, 2016, p. 122)
Results T-P w/Trans Cost (Moskowitz, 2016, p. 120) Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0634 ADT 0.0018 0.1372 -0.4290 0.2388 [-0.0362 ... 0.1010] 17/50 DyFor GP -0.0157 0.1101 -0.2690 0.1426 [-0.0463 ... 0.0639] 15/50 2001-2002 Buy & Hold -0.3339 ADT -0.1364 0.1014 -0.2964 0.1601 [-0.1645 ... -0.0631] 50/50 DyFor GP -0.1018 0.0819 -0.2810 0.0817 [-0.1245 ... -0.0426] 50/50 2003-2004 Buy & Hold 0.2970 ADT 0.1035 0.0653 -0.0603 0.2529 [0.0854 ... 0.1507] 0/50 DyFor GP 0.0489 0.0723 -0.1780 0.2156 [0.0289 ... 0.1012] 0/50 1999-2004 Buy & Hold -0.0189 ADT -0.0349 0.1933 -0.5395 0.4592 [-0.0884 ... 0.0187] 24/50 DyFor GP -0.0698 0.1413 -0.3597 0.2136 [-0.1089 ... -0.0306] 15/50
Results T-P wo/Trans Cost Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0634 ADT 0.0788 0.1071 -0.1106 0.3576 [0.0491 ... 0.1562] 27/50 DyFor GP 0.0807 0.1323 -0.1904 0.3408 [0.0440 ... 0.1763] 26/50 2001-2002 Buy & Hold -0.3339 ADT -0.0524 0.1026 -0.2674 0.1521 [-0.0808 ... 0.0218] 50/50 DyFor GP -0.0594 0.0862 -0.2314 0.1020 [-0.0833 ... 0.0029] 50/50 2003-2004 Buy & Hold 0.2970 ADT 0.1246 0.0782 -0.0132 0.3739 [0.1029 ... 0.1811] 2/50 DyFor GP 0.1233 0.0702 -0.0297 0.2783 [0.1038 ... 0.1740] 0/50 1999-2004 Buy & Hold -0.0189 ADT 0.1683 0.2005 -0.1946 0.6959 [0.1128 ... 0.2239] 39/50 DyFor GP 0.1568 0.1887 -0.2618 0.5762 [0.1045 ... 0.2091] 41/50 (Moskowitz, 2016, p. 124)
ADT vs DyFor GP vs Buy and Hold 750 850 950 1050 1150 1250 1350 1450 1550 1/4/1999 1/4/2000 1/4/2001 1/4/2002 1/4/2003 1/4/2004 With Transaction Costs, 50 run mean index value Dyfor.y_predicted ADT Sliding.y_predicted 750 850 950 1050 1150 1250 1350 1450 1550 1/4/1999 1/4/2000 1/4/2001 1/4/2002 1/4/2003 1/4/2004 Without Transaction Costs, 50 run mean index value Dyfor.y_predicted ADT Sliding.y_predicted ADT: +0.1683% DyFor GP: +0.1568% B&H: -0.0189% ADT: -0.349% DyFor GP: -0.698% B&H: -0.0189% (Moskowitz, 2016, p. 208) (Moskowitz, 2016, p. 213)
Advanced GP • Modularity • Automatically Defined Functions • Strongly-typed GP • Closure • Advanced techniques • Looping • Memory store • Lambdas • Recursion • Time series regimes (Moskowitz, 2016) • Design patterns (Moskowitz, 2016) (Koza, 1994, p. 74)
Genetic Algorithms • Non-differentiable / nonlinear optimization problem • Search for parameters, rules • Size and shape prescribed • Bit, Numeric, or other representations • Ex. Minimize 𝑥2 − 50𝑦 + 𝑧3 , x={0-31},y={0-31},z={0-15} 10011 11000 1011 00110 11010 1100 10010 11010 1100 00111 11000 1011 192 − 50 ∗ 24 + 113 =492 62 − 50 ∗ 26 + 123 =464 182 − 50 ∗ 26 + 123=752 72 − 50 ∗ 24 + 113=180
Linear GP • Sequence of imperative instructions • Register-based operations • Machine code, GPU Instructions (Poli et al.,2008, pp. 61-65)
Demo- Symbolic Regression Regime Change • Regime determining branch • Regime specific functions • Implements template method design pattern Demo o
Next Steps • MATLAB (GA only) • JGAP (Java) • DEAP (Python) • Roll your own • Evolutionary Signals
Not So Shameless Plug • Evolutionary Signals • Develop Buy/Sell signals using genetic programming • Minimal financial knowledge and no programming experience required • Goals • Much larger number of predictor series • Crowdsource models • Earn revenue from high performing models • Open beta testing • Visit www.gpsignals.com for more information
Questions? • Thank you! • Contact info: LinkedIn: infoblazer @infojester
References • Chen, S. H., Kuo, T. W., & Hoi, K. M. (2008). Genetic Programming and Financial Trading: How Much About “What We Know.” In Handbook of financial engineering (pp. 99–154). Springer US. doi:10.1007/978-0-387-76682-9 • Keane, A. J. (1996). THE DESIGN OF A SATELLITE BOOM WITH ENHANCED VIBRATION PERFORMANCE USING GENETIC ALGORITHM TECHNIQUES. The Journal of the Acoustical Society of America, 99(4), 2599–2603. • Koza, J. R. (1994). Genetic programming II: automatic discovery of reusable programs. MIT press. • Koza, J. ., Keane, M. A., Streeter, M. J., Mydlowec, W., Yu, J., & Lanza, G. (2006). Genetic programming IV: Routine human-competitive machine intelligence (Vol. 5). Springer. • Moskowitz, D. (2016). Automatically Defined Templates for Improved Prediction of Non- stationary, Nonlinear Time Series in Genetic Programming. Doctoral dissertation. Nova Southeastern University. Retrieved from http://nsuworks.nova.edu/gscis_etd/953. • Poli, R., Langdon, W. B., McPhee, N. F., & Koza, J. R. (2008). A field guide to genetic programming. Lulu. com.

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Prediction the stock market with genetic programming

  • 1. Predicting the Stock Market with Genetic Programming David Moskowitz, Ph.D. Infoblazer LLC Data Scientists in Stamford Westport January 25, 2016
  • 2. Disclaimer • The following is my opinion only • It is not the opinion of my employer • It is not related to any work done at my employer You should not make any decision, financial, investments, trading or otherwise, based on any of the information presented without undertaking independent due diligence and consultation with a professional broker or competent financial advisor. You understand that you are using any and all information presented at your own risk.
  • 3. Agenda • What is Genetic Programming? • Time Series Prediction • Stock Market Prediction • Other Issues • Modularity • Linear GP • Genetic Algorithms • Demonstrations
  • 4. What is Genetic Programming? • Get a computer to do something without telling it how to do it • Breeds a population of computer programs that improve over time • Evolution • Genetic Operators • Survival of the Fittest • Stochastic component • Non-Greedy • Creativity • Novel solutions • Size and shape of solution unknown • Limited only by what can be represented as a computer program (Koza et al., 2006, p. 11)
  • 5. Example: Design of a Satellite Boom • Designed using a genetic algorithm • 20,000+% improvement in frequency averaged energy levels (Keane, 1996)
  • 6. History • Visionaries • Samuel 1959 – Goal of AI • Turing 1948 – Evolutionary search, gene combination, survival of the fittest • Evolutionary Algorithms , 1962- • mutation , populations, • Genetic Algorithms, 1973- • John Holland • Crossover • Genetic Programming, 1989- • John Koza • Best way to represent a computer program is a computer program
  • 7. How GP Works • Preparatory Steps • Primitives • Fitness Function(s) • Initialize Population • Evolve Population • Calculate population fitness • Select next generation • Termination Condition (Poli et al.,2008, p. 2)
  • 8. GP Representation • LISP • (max (+ x x) (+ x (* 3 y))) • max(x+x,x+3*y) MAX X + + *X X 3 y
  • 9. GP Operations • Probabilistically select an operation • Crossover • Switch two nodes on different individuals • Mutation • Randomly modify an individual (node) • Reproduction • Copy parent, as is, to next generation
  • 10. GP Selection • Need to select one or two individuals for genetic operations • Selection is probabilistic • Fitness Proportional Selection • Tournament Selection
  • 11. Crossover + + X y 3 * + y 1 / X 2 + + X y 3 * + y 1 / X 2 Parents Children
  • 13. Demo – Symbolic Regression • Curve Fitting • 𝑥3 − 𝑥2 + 𝑥 − 4 • Prove that GP works -200000 0 200000 400000 600000 800000 1000000 1200000 0 10 20 30 40 50 60 70 80 90 Y X Demo a, b
  • 14. Chaotic Series • Look random, but are deterministic • Highly dependent on initial conditions • Difficult to predict 𝑌𝑡 = 𝑠𝑖𝑛 𝑥 − 130 + 𝑥 + 130 x=0: 𝑌0 = 0.9 X>0: 𝑌 𝑡+1 = 4𝑌𝑡(1 − 𝑌𝑡) 0 0.2 0.4 0.6 0.8 1 1.2 0 10 20 30 40 50 60 70 80 90 Y X 9 10 11 12 13 14 15 16 17 0 10 20 30 40 50 60 70 80 90 Y X
  • 15. Demo- Chaotic Series Symbolic Regression Demo c, d, e, f
  • 16. Regime Change • Goal is to uncover underlying data generating process • This can change over time -15 -10 -5 0 5 10 0 14 28 42 56 70 84 98 112 126 140 154 168 182 196 Y X 0<=x<70: 𝑌𝑡 = 𝑠𝑖𝑛 𝑥 + 𝑥 70<=x<130: 𝑌𝑡 = 𝑐𝑜𝑠 𝑥 − 𝑥 130<=x<200: 𝑌𝑡 = 𝑠𝑖𝑛 𝑥 − 130 + 𝑥 − 130 -3 -2 -1 0 1 2 3 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Y X x<200, x>=300: 𝑌 𝑡+1 = 4𝑌𝑡(1 − 𝑌𝑡) 200<=x<300: 𝑌 𝑡+1 = 1.8708𝑌𝑡 − 𝑌𝑡−1 S&P 500 index close price during the stock market crash of 2008 (Yahoo, 2013). 𝑌𝑡 = 𝑓 𝑊𝑇𝐹 ?
  • 17. Demo- Symbolic Regression Regime Change Demo g
  • 18. Time Series Prediction • Train on past values • Predict future values • Retrain periodically
  • 19. Demo- Chaotic Series Prediction Demo h, I, j
  • 20. Market Prediction • S&P 500 Long-Flat (Invest-don’t invest) • Ignore transaction costs • Ignore out of market returns • Predictors • S&P 500 Price • S&P 500 Volume • 250-day MA normalized 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 500 1000 1500 2000 2500 S&P 500 Index Series Index Value 250 Day Moving Average 250-day MA Normalized
  • 21. GP is a Perfect Match for Market Prediction • “The interrelationships among the relevant variables is unknown or poorly understood (or where it is suspected that the current understanding may possibly be wrong).” • “Finding the size and shape of the ultimate solution is a major part of the problem.” • “Significant amounts of test data are available in computer-readable form.” • “There are good simulators to test the performance of tentative solutions to a problem, but poor methods to directly obtain good solutions.” • “Conventional mathematical analysis does not, or cannot, provide analytic solutions” • “An approximate solution is acceptable (or is the only result that is ever likely to be obtained)” • “Small improvements in performance are routinely measured (or easily measurable) and highly prized.” (Poli et al.,2008, pp. 111-113)
  • 22. Primitive Set • Hundreds of indicators • Ex. (http://www.investopedia.com/active-trading/technical-indicators/) • Include common technical analysis indicators • Momentum- compare to recent average • Breakout- compare to recent minimum/maximum • Ex. Buy if current price risen by 2% over minimum price last 30 days • Prefer low level functions • Better results possible with higher level , packaged indicators?
  • 23. Primitive set • Functions • Add • Subtract • Multiply • Divide • Gt • Lt • And • Or • Not • offsetValue • ifElseBoolean • movingAverage • periodMaximum • periodMinimum • AbsoluteDifference • Terminals • randomInteger(low high) • randomDouble(low high) • True • False • offsetValue(0) • Hundreds of other technical indicators (http://www.investopedia.com/active- trading/technical-indicators/)
  • 24. Training Approaches • Train-Predict-Retrain • Train-Test-Predict • Multiple Runs Train M Test N Predict 1 Train Predict M N (1) Demo k, l, m
  • 25. Experiment- Market Prediction • Investment decisions in S&P 500 Index • Modeled after (Chen et al., 2008), 1988-2004 • Long-Flat decisions • Normalized by 250-day moving average • Fitness = investment gain 0 200 400 600 800 1000 1200 1400 1600 1988-01-04 1988-08-16 1989-03-31 1989-11-10 1990-06-27 1991-02-08 1991-09-24 1992-05-07 1992-12-18 1993-08-04 1994-03-17 1994-10-31 1995-06-15 1996-01-29 1996-09-11 1997-04-25 1997-12-08 1998-07-24 1999-03-10 1999-10-21 2000-06-06 2001-01-19 2001-09-04 2002-04-25 2002-12-06 2003-07-24 2004-03-09 2004-10-21 2005-06-07 S&P 500 0.7 0.8 0.9 1 1.1 1.2 1.3 1988-12-27 1989-08-10 1990-03-26 1990-11-06 1991-06-21 1992-02-04 1992-09-17 1993-05-03 1993-12-14 1994-07-29 1995-03-14 1995-10-25 1996-06-10 1997-01-22 1997-09-05 1998-04-22 1998-12-03 1999-07-21 2000-03-03 2000-10-16 2001-06-01 2002-01-22 2002-09-05 2003-04-22 2003-12-03 2004-07-21 2005-03-04 2005-10-17 2006-06-02 Normalized
  • 26. Experiment- Market Prediction • Training-validation-prediction approach (T-V-P) • Training-prediction approach (T-P) • Training - 1989-1998 • Prediction- 1999-2004 (Chen et al., 2008, p. 110)
  • 27. Results T-V-P w/Trans Cost Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0751 GP 0.0434 0.0664 -0.1917 0.1197 [0.0250 ... 0.0618] 5/50 ADF 0.0309 0.0798 -0.3054 0.0845 [0.0088 ... 0.0530] 3/50 ADT 0.0510 0.0519 -0.1974 0.1042 [0.0366 ... 0.0654] 5/50 2001-2002 Buy & Hold -0.3144 GP -0.3693 0.1306 -0.8087 -0.2885 [-0.4055 ... -0.3331] 1/50 ADF -0.3347 0.0887 -0.7290 -0.1777 [-0.3593 ... -0.3102] 2/50 ADT -0.3697 0.1390 -0.7450 -0.0134 [-0.4082 ... -0.3312] 1/50 2003-2004 Buy & Hold 0.3332 GP 0.2945 0.0497 0.1432 0.3291 [0.2807 ... 0.3083] 0/50 ADF 0.3139 0.0390 0.1170 0.3539 [0.3031 ... 0.3247] 1/50 ADT 0.3247 0.0150 0.2349 0.3522 [0.3205 ... 0.3289] 2/50 (Moskowitz, 2016, p. 119)
  • 28. Results T-V-P wo/Trans Cost Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0751 GP 0.1494 0.1088 -0.0438 0.4525 [0.1192 ... 0.1795] 35/50 ADF 0.1418 0.1238 -0.0399 0.5112 [0.1075 ... 0.1761] 35/50 ADT 0.1567 0.1099 -0.0068 0.4796 [0.1262 ... 0.1871] 37/50 2001-2002 Buy & Hold -0.3144 GP -0.3121 0.0573 -0.4081 -0.0348 [-0.3280 ... -0.2962] 17/50 ADF -0.3023 0.0848 -0.5153 0.0196 [-0.3258 ... -0.2788] 18/50 ADT -0.2843 0.0635 -0.3924 -0.1245 [-0.3020 ... -0.2667] 32/50 2003-2004 Buy & Hold 0.3332 GP 0.3045 0.0929 0.0463 0.5045 [0.2788 ... 0.3303] 15/50 ADF 0.3395 0.1171 -0.0016 0.5597 [0.3070 ... 0.3719] 22/50 ADT 0.3329 0.1202 0.0775 0.6443 [0.2996 ... 0.3663] 29/50 (Moskowitz, 2016, p. 122)
  • 29. Results T-P w/Trans Cost (Moskowitz, 2016, p. 120) Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0634 ADT 0.0018 0.1372 -0.4290 0.2388 [-0.0362 ... 0.1010] 17/50 DyFor GP -0.0157 0.1101 -0.2690 0.1426 [-0.0463 ... 0.0639] 15/50 2001-2002 Buy & Hold -0.3339 ADT -0.1364 0.1014 -0.2964 0.1601 [-0.1645 ... -0.0631] 50/50 DyFor GP -0.1018 0.0819 -0.2810 0.0817 [-0.1245 ... -0.0426] 50/50 2003-2004 Buy & Hold 0.2970 ADT 0.1035 0.0653 -0.0603 0.2529 [0.0854 ... 0.1507] 0/50 DyFor GP 0.0489 0.0723 -0.1780 0.2156 [0.0289 ... 0.1012] 0/50 1999-2004 Buy & Hold -0.0189 ADT -0.0349 0.1933 -0.5395 0.4592 [-0.0884 ... 0.0187] 24/50 DyFor GP -0.0698 0.1413 -0.3597 0.2136 [-0.1089 ... -0.0306] 15/50
  • 30. Results T-P wo/Trans Cost Method Mean Std. Dev. Min Max 95% CI # beating benchmark 1999-2000 Buy & Hold 0.0634 ADT 0.0788 0.1071 -0.1106 0.3576 [0.0491 ... 0.1562] 27/50 DyFor GP 0.0807 0.1323 -0.1904 0.3408 [0.0440 ... 0.1763] 26/50 2001-2002 Buy & Hold -0.3339 ADT -0.0524 0.1026 -0.2674 0.1521 [-0.0808 ... 0.0218] 50/50 DyFor GP -0.0594 0.0862 -0.2314 0.1020 [-0.0833 ... 0.0029] 50/50 2003-2004 Buy & Hold 0.2970 ADT 0.1246 0.0782 -0.0132 0.3739 [0.1029 ... 0.1811] 2/50 DyFor GP 0.1233 0.0702 -0.0297 0.2783 [0.1038 ... 0.1740] 0/50 1999-2004 Buy & Hold -0.0189 ADT 0.1683 0.2005 -0.1946 0.6959 [0.1128 ... 0.2239] 39/50 DyFor GP 0.1568 0.1887 -0.2618 0.5762 [0.1045 ... 0.2091] 41/50 (Moskowitz, 2016, p. 124)
  • 31. ADT vs DyFor GP vs Buy and Hold 750 850 950 1050 1150 1250 1350 1450 1550 1/4/1999 1/4/2000 1/4/2001 1/4/2002 1/4/2003 1/4/2004 With Transaction Costs, 50 run mean index value Dyfor.y_predicted ADT Sliding.y_predicted 750 850 950 1050 1150 1250 1350 1450 1550 1/4/1999 1/4/2000 1/4/2001 1/4/2002 1/4/2003 1/4/2004 Without Transaction Costs, 50 run mean index value Dyfor.y_predicted ADT Sliding.y_predicted ADT: +0.1683% DyFor GP: +0.1568% B&H: -0.0189% ADT: -0.349% DyFor GP: -0.698% B&H: -0.0189% (Moskowitz, 2016, p. 208) (Moskowitz, 2016, p. 213)
  • 32. Advanced GP • Modularity • Automatically Defined Functions • Strongly-typed GP • Closure • Advanced techniques • Looping • Memory store • Lambdas • Recursion • Time series regimes (Moskowitz, 2016) • Design patterns (Moskowitz, 2016) (Koza, 1994, p. 74)
  • 33. Genetic Algorithms • Non-differentiable / nonlinear optimization problem • Search for parameters, rules • Size and shape prescribed • Bit, Numeric, or other representations • Ex. Minimize 𝑥2 − 50𝑦 + 𝑧3 , x={0-31},y={0-31},z={0-15} 10011 11000 1011 00110 11010 1100 10010 11010 1100 00111 11000 1011 192 − 50 ∗ 24 + 113 =492 62 − 50 ∗ 26 + 123 =464 182 − 50 ∗ 26 + 123=752 72 − 50 ∗ 24 + 113=180
  • 34. Linear GP • Sequence of imperative instructions • Register-based operations • Machine code, GPU Instructions (Poli et al.,2008, pp. 61-65)
  • 35. Demo- Symbolic Regression Regime Change • Regime determining branch • Regime specific functions • Implements template method design pattern Demo o
  • 36. Next Steps • MATLAB (GA only) • JGAP (Java) • DEAP (Python) • Roll your own • Evolutionary Signals
  • 37. Not So Shameless Plug • Evolutionary Signals • Develop Buy/Sell signals using genetic programming • Minimal financial knowledge and no programming experience required • Goals • Much larger number of predictor series • Crowdsource models • Earn revenue from high performing models • Open beta testing • Visit www.gpsignals.com for more information
  • 38. Questions? • Thank you! • Contact info: LinkedIn: infoblazer @infojester
  • 39. References • Chen, S. H., Kuo, T. W., & Hoi, K. M. (2008). Genetic Programming and Financial Trading: How Much About “What We Know.” In Handbook of financial engineering (pp. 99–154). Springer US. doi:10.1007/978-0-387-76682-9 • Keane, A. J. (1996). THE DESIGN OF A SATELLITE BOOM WITH ENHANCED VIBRATION PERFORMANCE USING GENETIC ALGORITHM TECHNIQUES. The Journal of the Acoustical Society of America, 99(4), 2599–2603. • Koza, J. R. (1994). Genetic programming II: automatic discovery of reusable programs. MIT press. • Koza, J. ., Keane, M. A., Streeter, M. J., Mydlowec, W., Yu, J., & Lanza, G. (2006). Genetic programming IV: Routine human-competitive machine intelligence (Vol. 5). Springer. • Moskowitz, D. (2016). Automatically Defined Templates for Improved Prediction of Non- stationary, Nonlinear Time Series in Genetic Programming. Doctoral dissertation. Nova Southeastern University. Retrieved from http://nsuworks.nova.edu/gscis_etd/953. • Poli, R., Langdon, W. B., McPhee, N. F., & Koza, J. R. (2008). A field guide to genetic programming. Lulu. com.