Price prediction plays a crucial role in portfolio selection (PS). However, most price prediction strategies only make a single prediction and do not have efficient mechanisms to make a comprehensive price prediction. Here, we propose a comprehensive price prediction (CPP) system based on inverse multiquadrics (IMQ) radial basis function. First, the novel radial basis function (RBF) system based on IMQ function rather than traditional Gaussian (GA) function is proposed and centers on multiple price prediction strategies, aiming at improving the efficiency and robustness of price prediction. Under the novel RBF system, we then create a portfolio update strategy based on kernel and trace operator. To assess the system performance, extensive experiments are performed based on 4 data sets from different real-world financial markets. Interestingly, the experimental results reveal that the novel RBF system effectively realizes the integration of different strategies and CPP system outperforms other systems in investing performance and risk control, even considering a certain degree of transaction costs. Besides, CPP can calculate quickly, making it applicable for large-scale and time-limited financial market.
KeywordsComprehensive Price PredictionPortfolio Selection (PS)Inverse Multiquadrics (IMQ) Radial Basis Function
Kelly Jr., J. (1956) A New Interpretation of Information Rate. Bell System Technical Journal, 35, 917-926. https://doi.org/10.1002/j.1538-7305.1956.tb03809.x
Finkelstein, M. and Whitley, R. (1981) Optimal Strategies for Repeated Games. Advance in Applied Probability, 13, 415-428. https://doi.org/10.2307/1426692
Wilder, W. (2012) The ADAM Theory of Markets. Shanxi Peoples’s Publishing House.
Li, B. and Hoi, S.C.H. (2014) Online Portfolio Selection: A Survey. ACM Computing Surveys, 46, Article No. 35. https://doi.org/10.1145/2512962
Lai, Z.R., Dai, D.Q., Ren, C.X. and Huang, K.-K. (2018) A Peak Price Tarcking-Based Learning System for Portfolio Selection. IEEE Transactions Neural Newtworks and Learning Systems, 29, 2823-2832.
Borodin, A., EL-Yaniv, R. and Gogan, V. (2004) Can We Learn to Beat the Best Stock. Journal of Artificial Intelligence Research, 21, 579-694. https://doi.org/10.1613/jair.1336
Huang, D.-J., Zhou, J.-L. and Li, B. (2016) Robust Median Reversion Strategy for Online PS. IEEE Transactions Neural Newtworks and Learning Systems, 28, 2480-2493. https://doi.org/10.1109/TKDE.2016.2563433
Li, B., Hoi, S.C.H. and Zhao, P.-L. (2013) Confidence Weighted Mean Reversion Strategy for Online PS. ACM Transactions on Knowledge Discovery from Data, 7, Article No. 4. https://doi.org/10.1145/2435209.2435213
Li, B., Hoi, S.C.H., Sahoo, D. and Liu, Z.-Y. (2015) Moving Average Reversion Strategy for Online Portfolio Selection. Artificial Intelligence, 222, 104-123. https://doi.org/10.1016/j.artint.2015.01.006
Gyorfi, L., Urban, A. and Vajda, I. (2007) Kernel-Based Semi-Log-Optimal Empirical Empirical Portfolio Selection Strategies. International Journal Theoretical and Applied Finance, 10, 505-516. https://doi.org/10.1142/S0219024907004251
Gyorfi, L., Lugosi, G. and Udina, F. (2006) Nonparametric Kernel-Based Sequential Investment Strategies. Mathematical Finance, 16, 337-357. https://doi.org/10.1111/j.1467-9965.2006.00274.x
Gyorfi, L., Udina, F. and Walk, H. (2008) Nonparametric Nearest Neighbor Based Empirical Portfolio Selection Strategies. Statistics & Decisions, 26, 145-157. https://doi.org/10.1524/stnd.2008.0917
Abbasbandy, S., Roohani Ghehsateh, H., Hashim, I. and Alsaedi, A. (2014) A Comparision Study of Meshfree Techniques for Solving the Two-Dimensional Linear Hyperbolic Telegraph Equation. Engineering Analysis with Boundary Elements, 47, 10-20. https://doi.org/10.1016/j.enganabound.2014.04.006
Ji, Y. and Kim, S. (2013) An Adaptive Radial Basis Function Method Using Weighted Improvement. Winter Simulation Conference Proceeding, Washington DC, 8-11 December 2013, 957-968. https://doi.org/10.1109/WSC.2013.6721486
Khan, M., Khan, Z. and Khan, H. (2020) Collocation Method for Multiplicative Noise Removal Model. Mehran University Research Journal of Engineering and Technology, 39, 734-743. https://doi.org/10.22581/muet1982.2004.05
Ku, C.Y., Liu, C.Y. and Xiao, J.E. (2020) Multiquadrics without the Shape Parameter for Solving Partial Differential Equations. Symmetry, 12, Article No. 1813. https://doi.org/10.3390/sym12111813
Wang, S.Y. and Wang, M.Y. (2006) Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method. Computer Modeling in Engineering & Sciences, 13, 119-147.
Tanbay, T. and Ozgener, B. (2014) A Comparison of the Meshless RBF Collocation Method with Finite Element and Boundary Element Methods in Neutron Diffusion Calculation. Engineering Analysis with Boundary Elements, 46, 30-40. https://doi.org/10.1016/j.enganabound.2014.05.005
Soley, F., Barf, M. and Hagh, F. (2018) Inverse Multi-Quadric RBF for Computing the Weights of FD Method: Application to American Options. Communications in Nonlinear Science and Numerical Simulation, 64, 74-88. https://doi.org/10.1016/j.cnsns.2018.04.011
Tan, R., James, R. and Nina, F. (2020) Nonstationary Discrete Convolutionnkenel for Multimodeal Process Monitoring. IEEE Transaction on Neural Networks and Learning Systems, 31, 3670-3681. https://doi.org/10.1109/TNNLS.2019.2945847
Buhmann, D., Marchi, S. and Perra, E. (2020) Analysis of a New Class of Rational RBF Expansions. IMA Journal of Numerical Analysis, 40, 1972-1993. https://doi.org/10.1093/imanum/drz015
Hardy, R.L. (1990) Theory and Application of the Multiquadric-Biharmonic Method 20 Years of Discovery. Computers and Mathematics with Applications, 19, 163-208. https://doi.org/10.1016/0898-1221(90)90272-L
Franke, R. (1982) Scattered Data Interpolation: Tests of Some Methods. Mathematics of Computation, 38, 181-200. https://doi.org/10.1090/S0025-5718-1982-0637296-4
Weiszfeld, E. (1937) Sur le point pour lequel la somme des distance den points donnes est minimum. Tohoku Mathematical Journal, 43, 355-386.
Vard, Y. and Zhang, C.H. (2000) The Multivariate L1-Median and Associated data Depth. Proceedings of the National Academy of Science of the United States of America, 97, 1423-1426. https://doi.org/10.1073/pnas.97.4.1423
Boyd, J.P. (2011) The Near-Equivalence of Five Species of Spectrally-Accurate Radial Basis Functions (RBFs): Asymptotic Approximations to the RBF Cardinal Functions on a Uniform Unbounded Grid. Journal of Computational Physics, 230, 1304-1318. https://doi.org/10.1016/j.jcp.2010.10.038
Brahma, P., Wu, D.-P. and She, Y.-Y. (2016) Why Deep Learning Works: A Manifold Disentanglement Perspective. IEEE Transaction on Neural Networks and Learning Systems, 27, 1997-2008. https://doi.org/10.1109/TNNLS.2015.2496947
Jenni, R., Serkan, K. and Mon, G. (2016) Training Radial Basis Function Neural Networks for Classification via Class-Specific Clustering. IEEE Transaction on Neural Networks and Learning Systems, 27, 2458-2471. https://doi.org/10.1109/TNNLS.2015.2497286
John, D., Shai, S.-S. and Yor, S. (2008) Efficient Projections onto the l1-Ball for Learning in High Dimensions. International Conference on Machine Learning, Helsinki, 5-9 July 2008, 272-279.
Lai, Z.-R., Yang, P.-Y., Wu, X.-T. and Fang, L. (2018) Trend Representation Based Log-Density Regularization System for Portfolio Optimization. Pattern Recognition, 76, 14-24. https://doi.org/10.1016/j.patcog.2017.10.024
Lai, Z.-R., Yang, P.-Y., Fang, L.-D. and Wu, X.-T. (2018) Short-Term Sparse Portfolio Optimization Based on Alternating Direction Method of Multipliers. Journal of Machine Learning Research, 19, 63:1-63:28.
Lai, Z.-R., Dai, D.-Q., Ren, C.-X. and Huang, K.-K. (2018) Radial Basis Functions with Adaptive Input and Composite Trend Representation for PS. IEEE Transaction on Neural Networks and Learning Systems, 29, 6214-6226. https://doi.org/10.1109/TNNLS.2018.2827952
Jegadeesh, N. (1990) Evidence of Predictable Behavior of Security Returns. The Journal of Finance, 45, 881-898. https://doi.org/10.1111/j.1540-6261.1990.tb05110.x
Sharpe, W.F. (1964) Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19, 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x
Lintner, J. (1965) The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47, 13-37. https://doi.org/10.2307/1924119
Mossin, J. (1966) Equilibrium in a Capital Asset Market. The Econometric Society, 34, 768-783. https://doi.org/10.2307/1910098
Sharpe, W.F. (1966) Mutual Fund Performance. The Journal of Business, 39, 119-138. https://doi.org/10.1086/294846
Treynor, J.L. and Black, F. (1973) How to Use Security Analysis to Improve Portfolio Selection. The Journal of Business, 46, 66-86. https://doi.org/10.1086/295508
Blum, A. and Kalai, A. (1999) Univeral Portfolios with and without Transaction Costs. Machine Learning, 35, 193-205. https://doi.org/10.1023/A:1007530728748
Aldrige, I. (2013) High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems. 2nd Edition, Wiley, Hoboken. https://doi.org/10.1002/9781119203803