Trading through the RSI indicator with the application of genetic algorithms for implementation in the investment business sector
Main Article Content
Keywords
Investment strategies, stock markets, automatic trading, quantitative trading
Abstract
Objective: This study proposes a methodology for the literature on equity asset investment applied through Genetic Algorithms and their implementation in the business investment sector. Method: The study was conducted by simulating B&H, AT, and AG investment strategies on the equity index. The investment return maximization process for financial assets was developed using genetic algorithms based on equations defined in chromosome classification with gene-immersive operations. It began with a random population of individuals with chromosomes representing a solution to achieve the greatest return possible. Results: The application of algorithms with the RSI generated returns that were 9% and 16% higher than those with B&H and technical analysis, respectively, indicating a greater investment risk for B&H with a volatility of 17.6% but comparable to those shown by genetic algorithms and technical analysis. Discussions: An improved risk–return ratio and efficiency in the key parameters of Portfolio Theory is possible through investment strategies based on genetic algorithms, including the RSI oscillator. Conclusions: This study suggests that an improvement in the return on investment may be expected through the stop loss and take profit parameters and a range of motion of the asset price before taking a position.
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References
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Burduk, A., Musiał, K., Kochańska, J., & Łapczyńska, D. (2019). Tabu search and genetic algorithm for production process scheduling problem. Scientific Journal of Logistics, 15(2), 181-189. https://doi.org/10.17270/J.LOG.2019.315
Chen, Y., Mabu, S., & Hirasawa, K. (2011). Genetic relation algorithm with guided mutation for the large-scale portfolio optimization. Expert System with Applications, 38 (4), 3353-3363. https://doi.org/10.1016/j.eswa.2010.08.120
Cheng, C-H., Chen, T-L., & Wei, L-Y. (2010). A Hybrid model based on rough sets theory and genetic algorithms for stock price forecasting. Information Science, 180(9), 1610-1629. https://doi.org/10.1016/j.ins.2010.01.014
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Cohen, G., & Cabiri, E. (2015). ¿Can technical oscillators outperform the buy and hold strategy? Applied Economics, 47(30), 3189-3197. https://doi.org/10.1080/00036846.2015.1013609
Cortés-Villafradez, R. A., y Hernández-Luna, Y. (2014). Impacto del desarrollo del sistema financiero en el crecimiento económico en países emergentes durante el periodo 2001-2011. Equidad y Desarrollo 1(22), 99-120. https://doi.org/10.19052/ed.3252
Ding, S., Cui, T., Xiong, X., & Bai, R. (2020). Forecasting stock market return with nonlinearity: a genetic programming approach. J Ambient Intell Human Comput, 11, 4927–4939. https://doi.org/10.1007/s12652-020-01762-0
Drake, A. E., & Marks, R. E. (2002). Genetic algorithms in economics and finance: forecasting stock market prices and foreign exchange—a review. En, Chen SH. (eds). Genetic algorithms and genetic programming in computational finance (pp. 29-54). https://doi.org/10.1007/978-1-4615-0835-9_2
Evans, C., Pappas, K., & Xhafa, F. (2013). Utilizing artificial neural networks and genetic algorithms to build an algo-trading model for intra-day foreign exchange speculation. Mathematical and Computer Modelling, 58 (5-6), 1249-1266. https://doi.org/10.1016/j.mcm.2013.02.002
Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417. https://doi.org/10.2307/2325486
Farias-Nazário, R. T., Lima e Silva, J., Sobreiro, V. A., & Kimura, H. (2017). A literature review of technical analysis on stock markets. The Quarterly Review of Economics and Finance, 66, 115-126. https://doi.org/10.1016/j.qref.2017.01.014
Fernández-Rodríguez, F., González-Martel, C., & Sosvilla-Rivero, S. (2001). Optimization of technical rules by genetic algorithms: evidence from the Madrid stock market. [Documento de trabajo]. FEDEA. www.//.ftp://ftp.fedea.es/pub/Papers/2001/dt2001-14.pdf
Figueroa-Pelayo, A. P., y Gualdron-López, A. E. (2014). Importancia de los índices bursátiles en el mercado de Colombia. Innovando en la U, 5(6), 123-131. https://revistas.unilibre.edu.co/index.php/innovando/article/view/3880
Forrest, S. (1993). Genetic algorithms: Principles of adaptation applied to computation. Science 261 (August 13), 872- 878. https://doi.org/10.1126/science.8346439
Forrest, S. (1996). Genetic Algorithms. ACM Computing Surveys, 28(1), 77-80. https://dl.acm.org/doi/10.1145/234313.234350
García, M. C., Jalal, A. M., Garzón, L. A., & López, J. M. (2013). Methods for predicting stock indexes. Ecos de Economía, 17(37), 51-82. https://doi.org/10.17230/ecos.2013.37.3
Gold, S. (2015). The Viability of six popular technical analysis trading rules in determining effective buy and sell signals: MACD, AROON, RSI, SO, OBV, and ADL. Journal of Applied Financial Research, 2, 8-29.
Henrique, B. M., Sobreiro, V. A., & Kimura, H. (2019). Literature review: machine learning techniques applied to financial market prediction. Expert Systems with Applications, 124, 226-251. https://doi.org/10.1016/j.eswa.2019.01.012
Holland, J. H. (1975). Adaptation in natural and artificial systems. University of Michigan Press.
Holland, J. H. (1982). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. MIT Press.
Isidore, R., & Christie, P. (2018). Fundamental analysis versus technical analysis-A comparative review. Int J Recent Sci Res, 9(1), 23009-23013. http://dx.doi.org/10.24327/ijrsr.2018.0901.1380
Khan, M. A., Aman, Q., & Khan, N. (2016). Technical analysis: concept or reality?. Pakistan Business Review: 732-751.
Levine, R. (1997). Financial development and economic growth: views and agenda. Journal of Economic Literature, 35(2), 688-726. https://www.jstor.org/stable/2729790
Llorente-López, M. A. (2012). Programación Genética en Mercados Financieros - Construcción automática de reglas de inversión utilizando programación genética [Proyecto final, Universitat Politècnica de Catalunya, UPC]. Repositorio digital. https://upcommons.upc.edu/bitstream/handle/2099.1/14104/77634.pdf?sequence=1&isAllowed=y
Luukka, P., Pätäri, E., John, E., & Garanina, T. (2016). Performance of moving average trading rules in a volatile stock market: The Russian evidence. Emerging Markets Finance & Trade, 52(10), 2434- 2450. https://doi.org/10.1080/1540496X.2015.1087785
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 1952, 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Metghalchi, M., Chen, C., & Hayes, L. (2015). History of share prices and market efficiency of the Madrid general stock index. International Review of Financial Analysis, 40, 178-184. https://doi.org/10.1016/j.irfa.2015.05.016
Mohd-Nor, S., & Wickremasinghe, G. (2014). The profitability of MACD and RSI trading rules in the Australian stock market. Investment Management and Financial Innovations, 11(4), 194-199. https://www.businessperspectives.org/images/pdf/applications/publishing/templates/article/assets/6228/imfi_en_2014_04cont_Nor.pdf
Moosa, I., & Li, L. (2011). Technical and fundamental trading in the Chinese stock market: Evidence based on time-series and panel data. Emerging Markets Finance and Trade, 47 (Supplement 1), 23-31. https://doi.org/10.2753/REE1540-496X4701S103
Murphy, J. (1998). Technical analysis of the financial markets: a comprehensive guide to trading methods and applications. Pearson Professional Education.
Murphy, J. (2016). Análisis Técnico de los Mercados Financieros. Editorial Paidós.
Nti, I. K., Adekoya, A. F., & Weyori, B. A. (2020). A systematic review of fundamental and technical analysis of stock market predictions. Artificial Intelligence Review, (53), 3007–3057. https://doi.org/10.1007/s10462-019-09754-z
Papailias, F., & Thomakos, D. D. (2015). An improved moving average technical trading rule. Physica A: Statistical Mechanics and its Applications, 428, 458-469. https://doi.org/10.1016/j.physa.2015.01.088
Petrusheva, N., & Jordanoski, I. (2016). Comparative analysis between fundamental and technical analysis of stocks. Journal of Process Management - New Technologies, International, 4(2), 26-31. https://scindeks-clanci.ceon.rs/data/pdf/2334-735x/2016/2334-735x1602026p.pdf
Radeerom, M. (2014). Automatic trading system based on genetic algorithm and technical analysis for stock index. International Journal of Information Processing and Management (IJIPM), 5(4), 124-132.
Restrepo-Gaviria, A. M. (2015). El sistema financiero y su importancia en el crecimiento económicos. [Tesis de pregrado, Universidad Pontificia Bolivariana]. Repositorio Institucional UPB. http://hdl.handle.net/20.500.11912/2239
Rodrigues-Leles, M. C., Amaral-Mozelli, L., & Nogueira-Guimarães, H. (2017). A new trend-following indicator: Using SSA to design trading rules. Fluctuation and Noise Letters, 16(2), 1-16. https://doi.org/10.1142/S021947751750016X
Rosillo, R., De la Fuente, D., & Burgos, J. A. L. (2013). Technical analysis and the Spanish stock exchange: testing the RSI, MACD, momentum and stochastic rules using Spanish market companies. Applied Economics, 45(12), 1541-1550. https://doi.org/10.1080/00036846.2011.631894
Rosillo, R., Giner, J., & De la Fuente, D. (2014). Stock market simulation using support vector machines. Journal of Forecasting, 33 (6), 488-500. https://doi.org/10.1002/for.2302
Sevilla-Arias, A. (2012). Índice bursátil. https://bit.ly/3u5KvZi
Shangkun, D., Yizhou, S., & Akito, S. (2012). Robustness test of genetic algorithm on generating rules for currency trading, Procedia Computer Science, 13, 86-98. https://doi.org/10.1016/j.procs.2012.09.117
Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x
Straßburg, J., Gonzàlez-Martel, C., & Alexandrov, V. (2012). Parallel genetic algorithms for stock market trading rules. Procedia Computer Science, 9, 1306-1313. https://doi.org/10.1016/j.procs.2012.04.143
Suresh, A. S. (2013). A study of fundamental and technical analysis. International Journal of Marketing, Financial Services & Management Research. 2(5), 44-59.
Swain, K.R. (2012). Book Review: Technical Analysis Ideal for Beginners. Asia-Pacific Journal of Management Research and Innovation, 8(4), 537-538. https://doi.org/10.1177%2F2319510X13482021
Taylor, N. (2014). The rise and fall of technical trading rule success. Journal of Banking & Finance, 40, 286-302. https://doi.org/10.1016/j.jbankfin.2013.12.004
Tharavanij, P., Siraprapasiri, V., & Rajchamaha, K. (2015). Performance of technical trading rules. SpringerPlus, 4(1). 1-40. https://doi.org/10.1186/s40064-015-1334-7
Vora, M. N. (2011). Genetic algorithm for trading signal generation. Solution to trader’s dilemma: Is it right time to trade?. International Conference on Business and Economics Research, 1, 316-320. http://ipedr.com/vol1/68-G00012.pdf
Wang, C.-F., Liu, K., Shen, P.-P. (2020) A novel genetic algorithm for global optimization. Acta Mathematicae Applicatae Sinica, English Series, 36(2), 482-491.https://doi.org/10.1007/s10255-020-0930-7
Wang, L., An, H., Liu, X. & Huang, X. (2016). Selecting dynamic moving average trading rules in the crude oil futures market using a genetic approach. Applied Energy, 162, 1608-1618. https://doi.org/10.1016/j.apenergy.2015.08.132
Wilder, J. W. (1978). New concepts in technical trading systems. Trend Research.
Zapranis, A., & Tsinaslanidis, P. E. (2012). A novel, rule-based technical pattern identification mechanism: Identifying and evaluating saucers and resistant levels in the US stock market. Expert System with Applications, 39(7), 6301-6308. https://doi.org/10.1016/j.eswa.2011.11.079
AFI Escuela de Finanzas España. (2017). AFI guías. Análisis técnico-17. https://docero.es/doc/508v50
Agudelo Aguirre, A. A., Rojas Medina, R. A., & Duque Méndez, N. D. (2020). Machine learning applied in the stock market through the Moving Average Convergence Divergence (MACD) indicator. Investment Management and Financial Innovations, 17(4), 44-60. https://doi.org/10.21511/imfi.17(4).2020.05
Allen, F., & Karjalainen, R. (1999). Using genetic algorithms to find technical trading rules. Journal of Financial Economic, 51(2), 245-271. https://doi.org/10.1016/S0304-405X(98)00052-X
Boboc, I-A., & Dinică, M-C. (2013). An algorithm for testing the efficient market hypothesis. PLoS ONE, 8(10), e78177. https://doi.org/10.1371/journal.pone.0078177
Burduk, A., Musiał, K., Kochańska, J., & Łapczyńska, D. (2019). Tabu search and genetic algorithm for production process scheduling problem. Scientific Journal of Logistics, 15(2), 181-189. https://doi.org/10.17270/J.LOG.2019.315
Chen, Y., Mabu, S., & Hirasawa, K. (2011). Genetic relation algorithm with guided mutation for the large-scale portfolio optimization. Expert System with Applications, 38 (4), 3353-3363. https://doi.org/10.1016/j.eswa.2010.08.120
Cheng, C-H., Chen, T-L., & Wei, L-Y. (2010). A Hybrid model based on rough sets theory and genetic algorithms for stock price forecasting. Information Science, 180(9), 1610-1629. https://doi.org/10.1016/j.ins.2010.01.014
Chou, C.-C., & Lin, K.-S. (2019). A fuzzy neural network combined with technical indicators and its application to Baltic dry index forecasting. Journal of Marine Engineering & Technology, 18 (2), 82-91. https://doi.org/10.1080/20464177.2018.1495886
Cohen, G., & Cabiri, E. (2015). ¿Can technical oscillators outperform the buy and hold strategy? Applied Economics, 47(30), 3189-3197. https://doi.org/10.1080/00036846.2015.1013609
Cortés-Villafradez, R. A., y Hernández-Luna, Y. (2014). Impacto del desarrollo del sistema financiero en el crecimiento económico en países emergentes durante el periodo 2001-2011. Equidad y Desarrollo 1(22), 99-120. https://doi.org/10.19052/ed.3252
Ding, S., Cui, T., Xiong, X., & Bai, R. (2020). Forecasting stock market return with nonlinearity: a genetic programming approach. J Ambient Intell Human Comput, 11, 4927–4939. https://doi.org/10.1007/s12652-020-01762-0
Drake, A. E., & Marks, R. E. (2002). Genetic algorithms in economics and finance: forecasting stock market prices and foreign exchange—a review. En, Chen SH. (eds). Genetic algorithms and genetic programming in computational finance (pp. 29-54). https://doi.org/10.1007/978-1-4615-0835-9_2
Evans, C., Pappas, K., & Xhafa, F. (2013). Utilizing artificial neural networks and genetic algorithms to build an algo-trading model for intra-day foreign exchange speculation. Mathematical and Computer Modelling, 58 (5-6), 1249-1266. https://doi.org/10.1016/j.mcm.2013.02.002
Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417. https://doi.org/10.2307/2325486
Farias-Nazário, R. T., Lima e Silva, J., Sobreiro, V. A., & Kimura, H. (2017). A literature review of technical analysis on stock markets. The Quarterly Review of Economics and Finance, 66, 115-126. https://doi.org/10.1016/j.qref.2017.01.014
Fernández-Rodríguez, F., González-Martel, C., & Sosvilla-Rivero, S. (2001). Optimization of technical rules by genetic algorithms: evidence from the Madrid stock market. [Documento de trabajo]. FEDEA. www.//.ftp://ftp.fedea.es/pub/Papers/2001/dt2001-14.pdf
Figueroa-Pelayo, A. P., y Gualdron-López, A. E. (2014). Importancia de los índices bursátiles en el mercado de Colombia. Innovando en la U, 5(6), 123-131. https://revistas.unilibre.edu.co/index.php/innovando/article/view/3880
Forrest, S. (1993). Genetic algorithms: Principles of adaptation applied to computation. Science 261 (August 13), 872- 878. https://doi.org/10.1126/science.8346439
Forrest, S. (1996). Genetic Algorithms. ACM Computing Surveys, 28(1), 77-80. https://dl.acm.org/doi/10.1145/234313.234350
García, M. C., Jalal, A. M., Garzón, L. A., & López, J. M. (2013). Methods for predicting stock indexes. Ecos de Economía, 17(37), 51-82. https://doi.org/10.17230/ecos.2013.37.3
Gold, S. (2015). The Viability of six popular technical analysis trading rules in determining effective buy and sell signals: MACD, AROON, RSI, SO, OBV, and ADL. Journal of Applied Financial Research, 2, 8-29.
Henrique, B. M., Sobreiro, V. A., & Kimura, H. (2019). Literature review: machine learning techniques applied to financial market prediction. Expert Systems with Applications, 124, 226-251. https://doi.org/10.1016/j.eswa.2019.01.012
Holland, J. H. (1975). Adaptation in natural and artificial systems. University of Michigan Press.
Holland, J. H. (1982). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. MIT Press.
Isidore, R., & Christie, P. (2018). Fundamental analysis versus technical analysis-A comparative review. Int J Recent Sci Res, 9(1), 23009-23013. http://dx.doi.org/10.24327/ijrsr.2018.0901.1380
Khan, M. A., Aman, Q., & Khan, N. (2016). Technical analysis: concept or reality?. Pakistan Business Review: 732-751.
Levine, R. (1997). Financial development and economic growth: views and agenda. Journal of Economic Literature, 35(2), 688-726. https://www.jstor.org/stable/2729790
Llorente-López, M. A. (2012). Programación Genética en Mercados Financieros - Construcción automática de reglas de inversión utilizando programación genética [Proyecto final, Universitat Politècnica de Catalunya, UPC]. Repositorio digital. https://upcommons.upc.edu/bitstream/handle/2099.1/14104/77634.pdf?sequence=1&isAllowed=y
Luukka, P., Pätäri, E., John, E., & Garanina, T. (2016). Performance of moving average trading rules in a volatile stock market: The Russian evidence. Emerging Markets Finance & Trade, 52(10), 2434- 2450. https://doi.org/10.1080/1540496X.2015.1087785
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 1952, 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Metghalchi, M., Chen, C., & Hayes, L. (2015). History of share prices and market efficiency of the Madrid general stock index. International Review of Financial Analysis, 40, 178-184. https://doi.org/10.1016/j.irfa.2015.05.016
Mohd-Nor, S., & Wickremasinghe, G. (2014). The profitability of MACD and RSI trading rules in the Australian stock market. Investment Management and Financial Innovations, 11(4), 194-199. https://www.businessperspectives.org/images/pdf/applications/publishing/templates/article/assets/6228/imfi_en_2014_04cont_Nor.pdf
Moosa, I., & Li, L. (2011). Technical and fundamental trading in the Chinese stock market: Evidence based on time-series and panel data. Emerging Markets Finance and Trade, 47 (Supplement 1), 23-31. https://doi.org/10.2753/REE1540-496X4701S103
Murphy, J. (1998). Technical analysis of the financial markets: a comprehensive guide to trading methods and applications. Pearson Professional Education.
Murphy, J. (2016). Análisis Técnico de los Mercados Financieros. Editorial Paidós.
Nti, I. K., Adekoya, A. F., & Weyori, B. A. (2020). A systematic review of fundamental and technical analysis of stock market predictions. Artificial Intelligence Review, (53), 3007–3057. https://doi.org/10.1007/s10462-019-09754-z
Papailias, F., & Thomakos, D. D. (2015). An improved moving average technical trading rule. Physica A: Statistical Mechanics and its Applications, 428, 458-469. https://doi.org/10.1016/j.physa.2015.01.088
Petrusheva, N., & Jordanoski, I. (2016). Comparative analysis between fundamental and technical analysis of stocks. Journal of Process Management - New Technologies, International, 4(2), 26-31. https://scindeks-clanci.ceon.rs/data/pdf/2334-735x/2016/2334-735x1602026p.pdf
Radeerom, M. (2014). Automatic trading system based on genetic algorithm and technical analysis for stock index. International Journal of Information Processing and Management (IJIPM), 5(4), 124-132.
Restrepo-Gaviria, A. M. (2015). El sistema financiero y su importancia en el crecimiento económicos. [Tesis de pregrado, Universidad Pontificia Bolivariana]. Repositorio Institucional UPB. http://hdl.handle.net/20.500.11912/2239
Rodrigues-Leles, M. C., Amaral-Mozelli, L., & Nogueira-Guimarães, H. (2017). A new trend-following indicator: Using SSA to design trading rules. Fluctuation and Noise Letters, 16(2), 1-16. https://doi.org/10.1142/S021947751750016X
Rosillo, R., De la Fuente, D., & Burgos, J. A. L. (2013). Technical analysis and the Spanish stock exchange: testing the RSI, MACD, momentum and stochastic rules using Spanish market companies. Applied Economics, 45(12), 1541-1550. https://doi.org/10.1080/00036846.2011.631894
Rosillo, R., Giner, J., & De la Fuente, D. (2014). Stock market simulation using support vector machines. Journal of Forecasting, 33 (6), 488-500. https://doi.org/10.1002/for.2302
Sevilla-Arias, A. (2012). Índice bursátil. https://bit.ly/3u5KvZi
Shangkun, D., Yizhou, S., & Akito, S. (2012). Robustness test of genetic algorithm on generating rules for currency trading, Procedia Computer Science, 13, 86-98. https://doi.org/10.1016/j.procs.2012.09.117
Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x
Straßburg, J., Gonzàlez-Martel, C., & Alexandrov, V. (2012). Parallel genetic algorithms for stock market trading rules. Procedia Computer Science, 9, 1306-1313. https://doi.org/10.1016/j.procs.2012.04.143
Suresh, A. S. (2013). A study of fundamental and technical analysis. International Journal of Marketing, Financial Services & Management Research. 2(5), 44-59.
Swain, K.R. (2012). Book Review: Technical Analysis Ideal for Beginners. Asia-Pacific Journal of Management Research and Innovation, 8(4), 537-538. https://doi.org/10.1177%2F2319510X13482021
Taylor, N. (2014). The rise and fall of technical trading rule success. Journal of Banking & Finance, 40, 286-302. https://doi.org/10.1016/j.jbankfin.2013.12.004
Tharavanij, P., Siraprapasiri, V., & Rajchamaha, K. (2015). Performance of technical trading rules. SpringerPlus, 4(1). 1-40. https://doi.org/10.1186/s40064-015-1334-7
Vora, M. N. (2011). Genetic algorithm for trading signal generation. Solution to trader’s dilemma: Is it right time to trade?. International Conference on Business and Economics Research, 1, 316-320. http://ipedr.com/vol1/68-G00012.pdf
Wang, C.-F., Liu, K., Shen, P.-P. (2020) A novel genetic algorithm for global optimization. Acta Mathematicae Applicatae Sinica, English Series, 36(2), 482-491.https://doi.org/10.1007/s10255-020-0930-7
Wang, L., An, H., Liu, X. & Huang, X. (2016). Selecting dynamic moving average trading rules in the crude oil futures market using a genetic approach. Applied Energy, 162, 1608-1618. https://doi.org/10.1016/j.apenergy.2015.08.132
Wilder, J. W. (1978). New concepts in technical trading systems. Trend Research.
Zapranis, A., & Tsinaslanidis, P. E. (2012). A novel, rule-based technical pattern identification mechanism: Identifying and evaluating saucers and resistant levels in the US stock market. Expert System with Applications, 39(7), 6301-6308. https://doi.org/10.1016/j.eswa.2011.11.079
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Jul 31, 2022
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Agudelo Aguirre, A. A., Rojas Medina , R. A., & Duque Méndez, N. D. (2022). Trading through the RSI indicator with the application of genetic algorithms for implementation in the investment business sector. Desarrollo Gerencial, 14(2), 1–24. https://doi.org/10.17081/dege.14.2.5755
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Author Biography
Alberto Antonio Agudelo Aguirre, Universidad Nacional de Colombia, Manizales, Colombia