×

zbMATH — the first resource for mathematics

Dynamic mode decomposition for financial trading strategies. (English) Zbl 1400.91558
Summary: We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this case financial market dynamics, in an equation-free manner by decomposing the state of the system into low-rank terms whose temporal coefficients in time are known. By extracting key temporal coherent structures (portfolios) in its sampling window, it provides a regression to a best fit linear dynamical system, allowing for a predictive assessment of the market dynamics and informing an investment strategy. The data-driven analytics capitalizes on stock market patterns, either real or perceived, to inform buy/sell/hold investment decisions. Critical to the method is an associated learning algorithm that optimizes the sampling and prediction windows of the algorithm by discovering trading hot-spots. The underlying mathematical structure of the algorithms is rooted in methods from nonlinear dynamical systems and shows that the decomposition is an effective mathematical tool for data-driven discovery of market patterns.

MSC:
91G10 Portfolio theory
37E99 Low-dimensional dynamical systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
37L65 Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems
Software:
sapa
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Acar E. and Satchell S. (Eds.), Advanced Trading Rules, 2002 (Butterworth-Heinemann).
[2] Almgren, R. and Lorenz, J., Bayesian adaptive trading with a daily cycle. J. Trading, 2006, 1, 38-46.
[3] Avellaneda, M. and Lee, J.-H., Statistical arbitrage in the U.S. equities market. Quant. Finance, 2008, 10, 761-782. · Zbl 1194.91196
[4] Boyce W.E. and DiPrima R.C., Elementary differential equations, 9th ed.2009 (Wiley). · Zbl 0178.09001
[5] Brandouy, O., Delahaye, J.P. and Ma, L., A computational definition of financial randomness. Quant. Finance, 2014, 14, 761-770. · Zbl 1308.91184
[6] Bright, I., Lin, G. and Kutz, J.N., Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements. Phys. Fluids, 2013, 25, 127102. · Zbl 1320.76003
[7] Brooks, C., Rew, A.G. and Ritson, S., A trading strategy based on the lead-lag relationship between the ftse 100 spot index and the liffe traded ftse futures contract. Int. J. Forecasting, 2001, 17, 31-44.
[8] Brunton, S., Proctor, J. and Kutz, J.N., Compressive sampling and dynamic mode decomposition. J. Comput. Dyn., 2015. to appear. · Zbl 1347.94012
[9] Brunton, S., Tu, J., Bright, I. and Kutz, J.N., Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems. SIAM App. Dyn. Sys., 2014, 13, 1716-1732. · Zbl 1354.37078
[10] Cheng, X., Philip L. H. Yu, and W. K. Li. Basket trading under co-integration with the logistic mixture autoregressive model. Quant. Finance, 2011, 11, 1407-1419. · Zbl 1277.91166
[11] Chen, K., Tu, J. and Rowley, C., Variants of dynamic mode decomposition: boundary condition, Koopman, and fourier analyses. J. Nonlinear Sci., 2012, 22(6), 887-915. · Zbl 1259.35009
[12] Chiarella, C., He, X.-Z. and Hommes, C., A dynamic analysis of moving average rules. J. Econo. Dyn. Control, 2006, 30, 1729-1753. · Zbl 1162.91474
[13] Crockford N., An Introduction to Risk Management, 2nd ed.1986 (Woodhead-Faulkner).
[14] d’Aspremont, A., Identifying small mean-reverting portfolios. Quant. Finance, 2011, 11, 351-364. · Zbl 1232.91701
[15] Drew, M.E., Bianchi, R.J. and Polichronis, J., A test of momentum trading strategies in foreign exchange markets: Evidence from the g7. Global Bus. Econo. Rev., 2005, 7, 155-179.
[16] Duran, A. and Bommarito, M.J., A profitable trading and risk management strategy despite transaction cost. Quant. Finance, 2011, 11, 829-848.
[17] Elliott, R., Van der Hoek, J. and Malcolm, W., Pairs trading. Quant. Finance, 2005, 5, 271-276. · Zbl 1134.91415
[18] Frömmel, M., MacDonald, R. and Menkhoff, L., Markov switching regimes in a monetary exchange rate model. Econ. Model., 2005, 22, 485-502.
[19] Harris, R.D.F. and Yilmaz, F., A momentum trading strategy based on the low frequency component of the exchange rate. J. Banking Finance, 2009, 33, 1575-1585.
[20] Hua, J.-C., Roy, S., McCauley, J.L. and Gunaratne, G.H., Using dynamic mode decomposition to extract cyclic behavior in the stock market. Physica A, 2015. to appear.
[21] Iati R., The real story of trading software espionage. AdvancedTrading.com, 10 July 2009.
[22] Jarrow, R.A., Lando, D. and Turnbull, S.M., A markov model for the term structure of credit risk spreads. Rev. Financ. Stud., 1997, 10, 481-523.
[23] Koopman, B.O., Hamiltonian systems and transformation in hilbert space. Proc. Nat. Acad. Sci., 1931, 17(5), 315-318. · Zbl 0002.05701
[24] Kutz J.N., Data-driven Modeling and Scientific Computing: Methods for Integrating Dynamics of Complex Systems and Big Data, 2013 (Oxford Press). · Zbl 1280.65002
[25] Kutz, J.N., Fu, X. and Brunton, S.L., Multi-resolution dynamic mode decomposition, 2015. arXiv:1409.6358.
[26] Lo, A.W. and MacKinlay, A.C., When are contrarian profits due to stock market overreaction?Rev. Financial Stud., 1990, 3, 175-206.
[27] Mezić, I., Analysis of fluid flows via spectral properties of the Koopman operator. Ann. Rev. Fluid Mech., 2013, 45, 357-378. · Zbl 1359.76271
[28] Muller U.A., Olsen R., Gencay R., Dacorogna M. and Pictet O., An Introduction to High-Frequency Finance, 2001 (Academic Press).
[29] Percival D.B. and Walden A.T., Spectral analysis for physical applications, 1993 (Cambridge University Press). · Zbl 0796.62077
[30] Proctor, J.L., Brunton, B., Brunton, S. and Kutz, J.N., Exploiting sparsity and equation-free architectures in complex systems. Eur. Phys. J. Spec. Top., 2015, 223, 2665-2684.
[31] Proctor, J., Brunton, S. and Kutz, J.N., Dynamic mode decomposition with control. 2014. arXiv:1409.6358. · Zbl 1334.65199
[32] Rowley, C., Mezić, I., Bagheri, S., Schlatter, P. and Henningson, D., Spectral analysis of nonlinear flows. J. Fluid Mech., 2009, 641, 115-127. · Zbl 1183.76833
[33] Sarantis, N., On the short-term predictability of exchange rates: A bvar time-varying parameters approach. J. Banking Finance, 2006, 2257-2279, 30.
[34] Schmid, P., Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech., 2010, 656, 5-28. · Zbl 1197.76091
[35] Schmid, P., Li, L., Juniper, M. and Pust, O., Applications of the dynamic mode decomposition. Theor. Comput. Fluid Dyn., 2011, 25(1-4), 249-259. · Zbl 1272.76179
[36] Schmid P.J. and Sesterhenn J., Dynamic mode decomposition of numerical and experimental data, 61st Annual Meeting of the APS Division of Fluid Dynamics, American Physical Society, November 2008.
[37] Shen, P., Market timing strategies that worked. J. Portfolio Manage., 2003, 29, 57-68.
[38] Shik, T.C. and Chong, T.T.-L., A comparison of ma and rsi returns with exchange rate intervention. Appl. Econo. Lett., 2005=7, 14, 371-383.
[39] Shiryaeva, A., Xu, Z. and Zhoubc, X.Y., Thou shalt buy and hold. Quant. Finance, 2008, 8, 765-776. · Zbl 1154.91478
[40] Strozzia, F. and Zaldívar, J.-M., Comenges. Towards a non-linear trading strategy for financial time series. Chaos Solitons Fractals, 2006, 28, 601-615. · Zbl 1121.91407
[41] Tapiero C., Risk and Financial Management: Mathematical and Computational Methods, 2004 (Wiley). · Zbl 1103.91003
[42] The New York Times. Times topics: High-frequency trading. AdvancedTrading.com, 20 December 2012.
[43] Trefethen, L.N. and Bau, D., Numerical Linear Algebra., 1997 (SIAM: Philadelphia).
[44] Tu, J.H., Rowley, C.W., Kutz, J.N. and Shang, J.K., Spectral analysis of fluid flows using sub-nyquist-rate piv data. Exp. Fluids, 2014, 55(9), 1-13.
[45] Tu, J., Rowley, C., Luchtenberg, D., Brunton, S. and Kutz, J.N., On dynamic mode decomposition: theory and applications. J. Comput. Dyn., 2014, 1, 391-421. · Zbl 1346.37064
[46] Williams, M., Rowley, C.W. and Kevrekidis, I.G., A kernel-based approach to data-driven koopman spectral analysis. 2015. arXiv:1411.2260. · Zbl 1366.37144
[47] Woodward, G. and Anderson, H., Does beta react to market conditions? estimates of ‘bull’ and ‘bear’ betas using a nonlinear market model with an endogenous threshold parameter. J. Quant. Finance, 2009, 9, 913-924.
[48] Zawadowski, A.G., Andor, G. and Kertész, J., Short-term market reaction after extreme price changes of liquid stocks. J. Quant. Finance, 2006, 6, 283-295. · Zbl 1134.91559
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.