Forecasting Stock Market Indices with Recurrent Neural Networks

  • Maxwell J. Rhee
Part of the Lecture Notes in Statistics book series (LNS, volume 119)


A recurrent neural network is used to forecast the out-of-sample return of a stock market index. The use of an extensive information set and a stochastic minimization algorithm distinguishes this study from prior work. The data set encompasses daily observations from 1970 through 1993, with the following forecast exercise undertaken. For a variety of model sizes, the network task is to approximate the weekly, monthly or quarterly conditional mean return. These forecasts are conditioned on a daily information set containing a number of index-specific and market-wide variables, term structure and corporate bond yields, and calendar variables. Network performance is evaluated by out-of-sample normalized mean-squared error, sample statistics describing the joint distribution of forecasted and actual returns, and a test for market-timing ability. A further performance evaluation concerns the construction of trading portfolios with transaction costs. Finally, bootstrapping techniques are applied to construct surrogate distributions of the out-of-sample statistics. Neural network models are found to perform more than adequately when compared with a benchmark linear model, and are able to generate large risk-adjusted returns over simple buy-and-hold strategies.


Recurrent Neural Network Hide Unit Forecast Horizon Short Selling Stock Market Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Aarts, Emile H. L., and Jan Korst, 1989, Simulated Annealing and Boltzmann Machines. New York: J. Wiley & Sons, Inc.MATHGoogle Scholar
  2. Barron, A. R., 1991, Universal approximation bounds for superpositions of a sigmodial function, Technical Report No. 58, Department of Statistics, University of Illinois, Urbana-Champaign.Google Scholar
  3. Bollerslev, Tim, Ray Y. Chou, and Kenneth F. Kroner, 1992, ARCH modeling in finance: a review of theory and empirical evidence, Journal of Econometrics, 52, 5–59.MATHCrossRefGoogle Scholar
  4. Brock, William A., W. Davis Dechert, and Jose A. Scheinkman, 1987, A test for independence based on the correlation dimension, Department of Economics, University of Wisconsin, mimeo.Google Scholar
  5. —, David A. Hsieh, and Blake LeBaron, 1991, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence. Cambridge, MA: MIT Press.Google Scholar
  6. Chen, Tianping, and Hong Chen, 1993, Approximations of continuous functionals by neural networks with application to dynamic systems, IEEE Transactions on Neural Networks, 4, 910–918.CrossRefGoogle Scholar
  7. Cybenko, G., 1989, Approximations by superpositions of a sigmodial function, Mathematics of Control, Signals and Systems, 2, 303–314.MathSciNetMATHCrossRefGoogle Scholar
  8. Diebold, Francis X., and J. M. Nason, 1990, Nonparametric exchange rate prediction?, Journal of International Economics, 28, 315–332.CrossRefGoogle Scholar
  9. Efron, Bradley, 1982, The Jackknife, the Bootstrap and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia: SIAM.Google Scholar
  10. —, and Robert J. Tibshirani, 1993, An Introduction to the Bootstrap, London: Chapman & Hall.MATHGoogle Scholar
  11. Elman, Jeffrey L., 1990, Finding structure in time, Cognitive Science, 14, 179–212.CrossRefGoogle Scholar
  12. Fama, Eugene F., 1981, Stocks, real activity, inflation, and money, American Economic Review, 71, 545–565.Google Scholar
  13. —, 1990, Stock returns expected returns, and real activity, Journal of Finance, 45, 1089–1108.CrossRefGoogle Scholar
  14. —, and Kenneth R. French, 1989, Business conditions and expected stock returns on stocks and bonds, Journal of Financial Economics, 25, 23–49.CrossRefGoogle Scholar
  15. —, and Kenneth R. French, 1988a, Dividend yields and expected stock returns, Journal of Financial Economics, 22, 3–25.CrossRefGoogle Scholar
  16. —, and Kenneth R. French, 1988b, Permanent and temporary components of stock prices, Journal of Political Economy, 96, 247–273.Google Scholar
  17. —, and G. William Schwert, 1977, Asset returns and inflation, Journal of Financial Economics, 5, 115–146.CrossRefGoogle Scholar
  18. Gallant, A. Ronald, and Halbert White, 1988, A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Oxford: Basil Blackwell.Google Scholar
  19. —, 1992, On learning the derivatives of an unknown mapping with multilayer feedforward networks, Neural Networks, 5, 128–138.CrossRefGoogle Scholar
  20. Henriksson, Roy D., and Robert C. Merton, 1981, On market timing and investment performance, II: Statistical procedures for evaluating forecasting skills, Journal of Business, 54, 513–533.CrossRefGoogle Scholar
  21. Hertz, John, Anders Krogh, and Richard G. Palmer, 1991, Introduction to the Theory of Neural Computation. Santa Fe Institute Studies in the Sciences of Complexity, Lecture Notes Vol. I. Redwood City, CA: Addison-Wesley Publishing.Google Scholar
  22. Hornik, Kurt, Maxwell B. Stinchcombe, and Halbert White, 1989, Multilayer feedforward networks are universal approximators, Neural Networks, 2, 359–366.CrossRefGoogle Scholar
  23. Hsieh, David A., 1993, Implications of nonlinear dynamics for financial risk management, Journal of Financial and Quantitative Analysis, 28, 41–64.CrossRefGoogle Scholar
  24. Hutchinson, James M., Andrew W. Lo, and Tomaso Poggio, 1994, A nonparametric approach to pricing and hedging derivative securities via learning networks, Journal of Finance, 49, 851–890.CrossRefGoogle Scholar
  25. Jegadeesh, Narasimham, 1990, Evidence of predictable behavior of security returns. Journal of Finance, 45, 881–898.CrossRefGoogle Scholar
  26. —, 1991, Seasonality in stock price mean reversion: Evidence from the US and the UK, Journal of Finance, 46, 1427–1444.CrossRefGoogle Scholar
  27. Keim, Donald B., and Robert F. Stambaugh, 1986, Predicting returns in the stock and bond markets, Journal of Financial Economics, 17, 357–390.CrossRefGoogle Scholar
  28. Kuan, Chung-Ming., 1993, A recurrent Newton algorithm and its convergence properties, Department of Economics, University of Illinois, Faculty Working Paper No. 93-0139.Google Scholar
  29. —, Kurt Hornik, and Halbert White, 1993, A convergence result for learning in recurrent neural networks, Department of Economics, University of California, San Diego, mimeo.Google Scholar
  30. LeBaron, Blake, 1992, Some relations between volatility and serial correlation in stock market returns, Journal of Business, 65, 199–219.CrossRefGoogle Scholar
  31. Ljung, L., and T. Söderström, 1986, Theory and Practice of Recursive Estimation. Cambridge, MA: MIT Press.Google Scholar
  32. Robbins, H., and S. Munro, 1951, A stochastic approximation model, Annals of Mathematics, 22, 400–407.MATHGoogle Scholar
  33. Rumelhart, David E., J. L. McClelland, and the PDP Research Group, 1986, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 1: Foundations. Cambridge, MA: MIT Press.Google Scholar
  34. Schwarz, G., 1978, Estimating the dimension of a model, Annals of Statistics, 6, 461–464.MathSciNetMATHCrossRefGoogle Scholar
  35. Sharpe, William F., 1966, Mutual fund performance, Journal of Business, 39, 119–138.CrossRefGoogle Scholar
  36. Wahba, Grace, 1990, Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia: SIAM.MATHGoogle Scholar
  37. Weigend, Andreas S., Bernardo A. Huberman, and David E. Rumelhart, 1990, Predicting the future: a connectionist approach, International Journal of Neural Systems, 1, 193–209.CrossRefGoogle Scholar
  38. —, Bernardo A. Huberman, and David E. Rumelhart, 1992, Predicting sunspots and exchange rates with connectionist networks, in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubank, Santa Fe Institute Studies in the Sciences of Complexity, Proceedings Volume XII, 395–432.Google Scholar
  39. —, and Blake LeBaron, 1994, Evaluating neural network predictors by bootstrapping, Department of Computer Science, University of Colorado, mimeo.Google Scholar
  40. White, Halbert, 1988, Economic prediction using neural networks: the case of IBM stock prices, Proceedings of the IEEE Second Conference on Neural Networks, II, 451–458, San Diego, CA: SOS Printing.Google Scholar
  41. —, 1992, Artificial Neural Networks: Approximation and Learning Theory. Cambridge, MA: Blackwell Publishers.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Maxwell J. Rhee
    • 1
  1. 1.BNP/Cooper Neff, Inc.RadnorUSA

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