Forex Daytrading Strategy : An Application of the Gaussian Mixture Model to Marginalized Currency pairs
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Abstract
In this article, we build a Daytrading strategy by applying a Gaussian Mixture Model (GMM) to so-called “marginalized” African currency pairs. With a sample of data covering the period of 01/01/2010 to 05/15/2021 and downloaded in real time from the US Federal Reserve (FRED) website and the Yahoo Finance platform, we found that by including four explanatory variables in the Gaussian mixture model, the GMM independently estimates the returns of the following six African currency pairs with an average accuracy of approximately 56.379%: USDZAR, USDNGN, USDEGP, USDMAD, USDMUR and USDKES. The accuracy of the estimations obtained with the GMM on the returns of the USDZAR currency pair is the highest (73.887%) among the six currency pairs studied in this work. Based on the above results, we have built a trading robot (based on the GMM) that runs in real time and which we have deployed in production in the exchange rate market. In general, by adjusting several parameters of the GMM, our trading robot achieves overall positive daily gains.
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Yvan Jorel Ngaleu Ngoyi, & Elie Ngongang. (2023). Forex Daytrading Strategy : An Application of the Gaussian Mixture Model to Marginalized Currency pairs. MULTIDISCIPLINARY JOURNAL OF INSTRUCTION (MDJI), 5(3), 1-44. Retrieved from https://journal.mdji.org/index.php/MDJI/article/view/169
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References
Adam Smith (1759); Theory of Moral Sentiments
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Bank of International Settlement, (2019), Triennial Central Bank Survey-Foreign exchange and derivatives market activity in 2019.
Baum, L.E.; Petrie, T. (1966). "Statistical Inference for Probabilistic Functions of Finite State Markov Chains"
BIS Papers No 90; Foreign exchange liquidity in the Americas; https://www.bis.org/publ/bppdf/bispap90.pdf; March 2017
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Chan Ernest and Belov Sergei and Ciobanu Radu, Conditional Parameter Optimization: Adapting a Strategy to Different Market Regimes (April 14, 2021). Available at SSRN: https://ssrn.com/abstract=3880643; https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3880643; https://www.predictnow.ai/blog/conditional-parameter-optimization-adapting-parameters-to-changing-market-regimes/
David Guerreiro: FOREIGN EXCHANGE MARKET BASICS: Financial Techniques; Year 2015-2016 Paris 8 University; david.guerreiro@univ-paris8.fr
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Demsetz, H. (1968). The costs of transacting. Quarterly Journal of Economics, Vol.82, 33-53.
Douglas A. Reynolds et al: Speaker Verification Using Adapted Gaussian Mixture Models; M.I.T. Lincoln Laboratory, 244 Wood St., Lexington, Mass. 02420; Digital Signal Processing 10, 19–41 (2000)
Eriksson, S. and Roding, C., (2007), Algorithmic Trading Uncovered - Impacts on an Electronic Exchange of Increasing Automation in Futures Trading, Royal Institute of Technology, Stockholm.
Eugène Fama: "Efficient Capital Market: a Review of Theorical and empirical Works", 1970
German, M.B. (1976). Market microstructure. Journal of Financial Economics, 3, pp 257-275
Hamilton, James D. “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica, vol. 57, no. 2, 1989, p. 357–84.
Hendershott, T., (2003), Electronic Trading in Financial Markets, IEEE Computer Science.
Jake Vanderplas: "Python Data Science Handbook "ESSENTIAL TOOLS FOR WORKING WITH DATA [2016]; [p. 476 to 488]
John B. Taylor (January 1999) “A Historical Analysis of Monetary Policy Rules”; p. 319 – 348; URL: https://www.nber.org/system/files/chapters/c7419/c7419.pdf
John B. Taylor, Discretion versus policy rules in practice (1993), Stanford University, y, Stanford, CA 94905
Johnson, N.L. (1949). "Bivariate Distributions Based on Simple Translation Systems".
Johnson, N.L. (1949). "Systems of Frequency Curves Generated by Methods of Translation"; https://www.jstor.org/stable/pdf/2332539.pdf
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Lars Peter Hansen: "Large sample properties of generalized method of moments estimators". Vol.50, No. 4 (July 1982) p. 1029-1054
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Laurence Broze: Scoring methods and risk management; University of Lille 3; https://moodle.univ-lille3.fr/pluginfile.php/392292/mod_resource/content/1/Credit2016.pdf; 2016-2017
Lexis Fauth: High Frequency Trading Modeling and Statistical Arbitrage; University of Lille I; Master 2 Mathematics and Finance Mathematics of Risk 2012/2013
Lofgren, Karl-Gustaf, et al. “Markets with Asymmetric Information: The Contributions of George Akerlof, Michael Spence and Joseph Stiglitz.” The Scandinavian Journal of Economics, vol. 104, no. 2, 2002, p. 195–211. JSTOR, http://www.jstor.org/stable/3441066.
Lovjit Thukral, Hélyette German et al: "A daily Trading strategy in the ETN space", summer 2013, journal of trading.
Markov, A. A. 1913. An example of statistical investigation of the text Eugene Onegin concerning the connection of samples in chains. (In Russian.) Bulletin of the Imperial Academy of Sciences of St. Petersburg 7(3):153–162. Unpublished English translation by Morris Halle, 1955. English translation by Alexander Y. Nitussov, Lioudmila Voropai, Gloria Custance and David Link, 2006. Science in Context 19(4):591–600.
Michael L. Halls Moore-"Advanced Algorithmic Trading" (2017); Professional Quant Trading Strategies With Advanced Statistical Techniques; Bayesian statistics, time series analysis and machine learning for profitable strategies.
Mundell, Robert A. (1963). "Capital mobility and stabilization policy under fixed and flexible exchange rates". Canadian Journal of Economics and Political Science.
Muth, John F. “Rational Expectations and the Theory of Price Movements.” Econometrica, vol. 29, no. 3, 1961, p. 315–35. JSTOR, https://doi.org/10.2307/1909635.
Patrik Idvall, Conny Jonsson; Algorithmic Trading: Hidden Markov Models on Foreign Exchange Data; LiTH - MAT - EX - - 08 / 01 - - SE
PREDICTION OF FINANCIAL TIME SERIES WITH HIDDEN MARKOV MODELS by Yingjian Zhang; B.Eng. Shandong University, China, 2001
Psychology of Great Traders, Thami Kabbaj (Author); Published in September 2011 Study (paperback)
R. Brealey, M. Myers et al: Principles of Financial Management; 8th edition; 2006
Robert Lucas, (1970), Capacity, overtime and empirical production functions, American Economic Review, 60, (2), 23-27
Rüdiger Dornbusch (1976). "Expectations and dynamics of the exchange rate". Journal of Political Economy. 84 (6): pp. 1161–1176.
Steve Renals and Peter Bell: "Hidden Markov models and Gaussian mixture models"; Automatic Speech Recognition— ASR Conferences 4&5 January 28/31, 2013;
Stiglitz, Joseph E. “Information and Economic Analysis: A Perspective”. The Economic Review, vol. 95, 1985, p. 21–41. JSTOR, https://doi.org/10.2307/2232867.
Taleb, Nassim Nicholas (2018). "Introduction". The skin in the game: hidden asymmetries in everyday life.
Thami Kabbaj: Psychology of Great Traders; Published in September 2011 Study (paperback)
The summation of random causes as a source of cyclical processes E. Slutzy 1927 Problems of economic conditions The Conjuncture Institute, Moscow vol 3 (1); published in English in Econometrica Vol. 5 (2) April 1937, p. 105-146
Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science, 211, 453-458
Valérie Monbet - 2011: "Modelling time series", 2011. pp 30-39
Wald, A. and Wolfowitz, J. (1940), "On a test whether two samples are from the same population," Ann. Mathematical Statist. 11, 147-162.
Wang, Shixiong; Li, Chongshou; Lim, Andrew (2019-12-18). "Why ARIMA and SARIMA are not enough". https://arxiv.org/pdf/1904.07632.pdf
Noel, Udny. 1927. On a method of investigating periodicities in perturbed series with special reference to Wolfer sunspot numbers. Philosophical Transactions 226: 267-298.
Zeljko Ivezic, Andrew J. Connoly, Jacob T. Vanderplas, and Alexander Gray: "Statistics, Data Mining, and Machine Learning in Astronomy". A PRACTICAL PYTHON GUIDE TO SURVEY DATA ANALYSIS. Princeton University Press. [2014]. [p.134 to 139]
Zoran Zivkovic: Improved adaptive Gaussian mixture model for background subtraction; Intelligent and Autonomous Systems Group; University of Amsterdam, Netherlands; In Proc. ICRP, 2004
Adam Smith (1776); Researches on the nature and causes of the wealth of nations
Akerlof, George A. “The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism.” The Quarterly Journal of Economics, vol. 84, no. 3, 1970, p. 488–500. JSTOR, https://doi.org/10.2307/1879431. In American slang, a lemon is a car that is found to be defective after it has been bought.
Ali El Attar. Robust estimation of mixing models on distributed data. Learning [cs.LG]. University of Nantes, 2012. French.
Arthur Charpentier: Time series forecasting models; UQAM, ACT6420, Winter 2011; May 15, 2012; charpentier.arthur@uqam.ca, url: http://freakonometrics.blog.free
Bank of International Settlement, (2004), BIS Quarterly Review – International banking and financial market developments.
Bank of International Settlement, (2019), Triennial Central Bank Survey-Foreign exchange and derivatives market activity in 2019.
Baum, L.E.; Petrie, T. (1966). "Statistical Inference for Probabilistic Functions of Finite State Markov Chains"
BIS Papers No 90; Foreign exchange liquidity in the Americas; https://www.bis.org/publ/bppdf/bispap90.pdf; March 2017
Carl Edward Rasmussen: The Infinite Gaussian Mixture Model; Department of Mathematical Modeling; Technical University of Denmark; Building 321, DK-2800 Kongens Lyngby, Denmark carl@imm.dtu.dk; MIT Press (2000); https://groups.seas.harvard.edu/courses/cs281/papers/rasmussen-1999a.pdf
Chan Ernest and Belov Sergei and Ciobanu Radu, Conditional Parameter Optimization: Adapting a Strategy to Different Market Regimes (April 14, 2021). Available at SSRN: https://ssrn.com/abstract=3880643; https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3880643; https://www.predictnow.ai/blog/conditional-parameter-optimization-adapting-parameters-to-changing-market-regimes/
David Guerreiro: FOREIGN EXCHANGE MARKET BASICS: Financial Techniques; Year 2015-2016 Paris 8 University; david.guerreiro@univ-paris8.fr
Davis, Mark, and Alison Etheridge. “Mathematics and Finance.” Louis Bachelier's Theory of Speculation: The Origins of Modern Finance, Princeton University Press, 2006, pp. 1–14. JSTOR, http://www.jstor.org/stable/j.ctt7scn4.5.
Demsetz, H. (1968). The costs of transacting. Quarterly Journal of Economics, Vol.82, 33-53.
Douglas A. Reynolds et al: Speaker Verification Using Adapted Gaussian Mixture Models; M.I.T. Lincoln Laboratory, 244 Wood St., Lexington, Mass. 02420; Digital Signal Processing 10, 19–41 (2000)
Eriksson, S. and Roding, C., (2007), Algorithmic Trading Uncovered - Impacts on an Electronic Exchange of Increasing Automation in Futures Trading, Royal Institute of Technology, Stockholm.
Eugène Fama: "Efficient Capital Market: a Review of Theorical and empirical Works", 1970
German, M.B. (1976). Market microstructure. Journal of Financial Economics, 3, pp 257-275
Hamilton, James D. “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.” Econometrica, vol. 57, no. 2, 1989, p. 357–84.
Hendershott, T., (2003), Electronic Trading in Financial Markets, IEEE Computer Science.
Jake Vanderplas: "Python Data Science Handbook "ESSENTIAL TOOLS FOR WORKING WITH DATA [2016]; [p. 476 to 488]
John B. Taylor (January 1999) “A Historical Analysis of Monetary Policy Rules”; p. 319 – 348; URL: https://www.nber.org/system/files/chapters/c7419/c7419.pdf
John B. Taylor, Discretion versus policy rules in practice (1993), Stanford University, y, Stanford, CA 94905
Johnson, N.L. (1949). "Bivariate Distributions Based on Simple Translation Systems".
Johnson, N.L. (1949). "Systems of Frequency Curves Generated by Methods of Translation"; https://www.jstor.org/stable/pdf/2332539.pdf
Jun Cai: A Markov Model of Switching-Regime ARCH; Journal of Business & Economic Statistics, Vol. 12, No. 3. (Jul., 1994), p. 309-316
Lars Peter Hansen: "Large sample properties of generalized method of moments estimators". Vol.50, No. 4 (July 1982) p. 1029-1054
Laurence Broze: Econometrics of finance and nonlinear time series; University of Lille 3; https://moodle.univ-lille3.fr/pluginfile.php/381970/mod_resource/content/1/Poly1_2016.pdf; 2016-2017
Laurence Broze: Scoring methods and risk management; University of Lille 3; https://moodle.univ-lille3.fr/pluginfile.php/392292/mod_resource/content/1/Credit2016.pdf; 2016-2017
Lexis Fauth: High Frequency Trading Modeling and Statistical Arbitrage; University of Lille I; Master 2 Mathematics and Finance Mathematics of Risk 2012/2013
Lofgren, Karl-Gustaf, et al. “Markets with Asymmetric Information: The Contributions of George Akerlof, Michael Spence and Joseph Stiglitz.” The Scandinavian Journal of Economics, vol. 104, no. 2, 2002, p. 195–211. JSTOR, http://www.jstor.org/stable/3441066.
Lovjit Thukral, Hélyette German et al: "A daily Trading strategy in the ETN space", summer 2013, journal of trading.
Markov, A. A. 1913. An example of statistical investigation of the text Eugene Onegin concerning the connection of samples in chains. (In Russian.) Bulletin of the Imperial Academy of Sciences of St. Petersburg 7(3):153–162. Unpublished English translation by Morris Halle, 1955. English translation by Alexander Y. Nitussov, Lioudmila Voropai, Gloria Custance and David Link, 2006. Science in Context 19(4):591–600.
Michael L. Halls Moore-"Advanced Algorithmic Trading" (2017); Professional Quant Trading Strategies With Advanced Statistical Techniques; Bayesian statistics, time series analysis and machine learning for profitable strategies.
Mundell, Robert A. (1963). "Capital mobility and stabilization policy under fixed and flexible exchange rates". Canadian Journal of Economics and Political Science.
Muth, John F. “Rational Expectations and the Theory of Price Movements.” Econometrica, vol. 29, no. 3, 1961, p. 315–35. JSTOR, https://doi.org/10.2307/1909635.
Patrik Idvall, Conny Jonsson; Algorithmic Trading: Hidden Markov Models on Foreign Exchange Data; LiTH - MAT - EX - - 08 / 01 - - SE
PREDICTION OF FINANCIAL TIME SERIES WITH HIDDEN MARKOV MODELS by Yingjian Zhang; B.Eng. Shandong University, China, 2001
Psychology of Great Traders, Thami Kabbaj (Author); Published in September 2011 Study (paperback)
R. Brealey, M. Myers et al: Principles of Financial Management; 8th edition; 2006
Robert Lucas, (1970), Capacity, overtime and empirical production functions, American Economic Review, 60, (2), 23-27
Rüdiger Dornbusch (1976). "Expectations and dynamics of the exchange rate". Journal of Political Economy. 84 (6): pp. 1161–1176.
Steve Renals and Peter Bell: "Hidden Markov models and Gaussian mixture models"; Automatic Speech Recognition— ASR Conferences 4&5 January 28/31, 2013;
Stiglitz, Joseph E. “Information and Economic Analysis: A Perspective”. The Economic Review, vol. 95, 1985, p. 21–41. JSTOR, https://doi.org/10.2307/2232867.
Taleb, Nassim Nicholas (2018). "Introduction". The skin in the game: hidden asymmetries in everyday life.
Thami Kabbaj: Psychology of Great Traders; Published in September 2011 Study (paperback)
The summation of random causes as a source of cyclical processes E. Slutzy 1927 Problems of economic conditions The Conjuncture Institute, Moscow vol 3 (1); published in English in Econometrica Vol. 5 (2) April 1937, p. 105-146
Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science, 211, 453-458
Valérie Monbet - 2011: "Modelling time series", 2011. pp 30-39
Wald, A. and Wolfowitz, J. (1940), "On a test whether two samples are from the same population," Ann. Mathematical Statist. 11, 147-162.
Wang, Shixiong; Li, Chongshou; Lim, Andrew (2019-12-18). "Why ARIMA and SARIMA are not enough". https://arxiv.org/pdf/1904.07632.pdf
Noel, Udny. 1927. On a method of investigating periodicities in perturbed series with special reference to Wolfer sunspot numbers. Philosophical Transactions 226: 267-298.
Zeljko Ivezic, Andrew J. Connoly, Jacob T. Vanderplas, and Alexander Gray: "Statistics, Data Mining, and Machine Learning in Astronomy". A PRACTICAL PYTHON GUIDE TO SURVEY DATA ANALYSIS. Princeton University Press. [2014]. [p.134 to 139]
Zoran Zivkovic: Improved adaptive Gaussian mixture model for background subtraction; Intelligent and Autonomous Systems Group; University of Amsterdam, Netherlands; In Proc. ICRP, 2004