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Applied Computational Intelligence Laboratory at Texas Tech University
Time series prediction using neural networks
Time series prediction using neural networks
Samy Bengio
Let a given one-variable time series be represented by the N values x(1), x(2), ..., x(N). Prediction then consists to find the future values x(N+1), x(N+2), ... Takens [6] has shown that if the series is obtained from a deterministic dynamical system, there exists a scalar d (which is called the embedding dimension), a scalar tau (which is an arbitrary delay) and a function f such that for every t > d tau:
x(t) = f(x(t-tau),x(t-2tau),...,x(t-dtau))
Then the prediction problem consists, given the first N values of a time series, to find the appropriate d, tau and f. Of course one usually cannot be sure that a given series is deterministic. Actually, statistical methods do exist to verify if a series is deterministic and to find d as well as tau but they require the size of the series to be on the order of 10**d which is rarely the case in practical problems. For the moment, let us assume that we know d and tau and that we want to find f. This is where neural networks come in: it is a well known fact that they can be used as universal function approximators [2,5].
However, these results are valid if and only if there is a sufficiently high number of training data in the series. In the other case, one could overtrain and prediction accuracy could deteriorate. This problem is known as the generalization problem and is well addressed by the works of Vapnik [7], which finds an upper bound of generalization error as a function of the number of free parameters in the learning system, the size of the training set, the training error and prior information given to the system.
For more information about our work, refer to the following publications: [1,3,4].
1 S. Bengio, F. Fessant, and D. Collobert. A Connectionist System for Medium-Term Horizon Time Series Prediction. In International Workshop on Applications of Neural Networks to Telecommunications, Stockholm, Sweden, 1995.
2 G. Cybenko. Approximation by superposition of sigmoidal functions. Mathematics of Control, Signal and Systems, 2:303--314, 1989.
3 F. Fessant, S. Bengio, and D. Collobert. On the Prediction of Solar Activity Using Different Neural Network Models. Annales Geophysicae, 1995.
4 F. Fessant, S. Bengio, and D. Collobert. Use of Modular Architectures for Time Series Prediction. Neural Processing Letters, 1995.
5 K. Hornik, M. Stinchcombe, and H. White. Multilayer feedforward networks are universal approximators. Neural Networks, 2:359--366, 1989.
6 F. Takens. Detecting strange attractors in turbulence. In D. A. Rand and L.-S. Young, editors, Dynamical Systems and Turbulence, volume 898 of Lecture Notes in Mathematics, pages 366--381, Warwick 1980, 1981. Springer-Verlag, Berlin.
7 V. N. Vapnik. Estimation of Dependencies Based on Empirical Data. Springer-Verlag, New-York, NY, USA, 1982.
Samy Bengio Tue Nov 7 20:04:22 EST 1995
The information revolution is generating mountains of data, from sources as diverse as credit card transactions, telephone calls, Web clickstreams, space science, and human genome research. At the same time, faster and cheaper storage technology lets us store greater amounts of data online, and better database-management-system software provides easy access to those databases.
Formerly Neurovest Journal now The Journal of Computational Intelligence in Finance - Hosted by The Finance & Technology Web. This is a great place to learn about nonlinear forecasting
techniques.
A CONSTRAINED NEURAL NETWORK KALMAN FILTER FOR PRICE ESTIMATION IN HIGH FREQUENCY FINANCIAL DATA
In this paper we present a neural network extended Kalman filter for modeling noisy financial time series. The neural network is employed to estimate the nonlinear dynamics of the extended Kalman filter. Conditions for the neural network weight matrix are provided to guarantee the stability of the filter. The extended Kalman filter presented is designed to filter three types of noise commonly observed in financial data: process noise, measurement noise, and arrival noise. The erratic arrival of data (arrival noise) results in the neural network predictions being iterated into the future. Constraining the neural network to have a fixed point at the origin produces better iterated predictions and more stable results. The performance of constrained and unconstrained neural networks within the extended Kalman filter is demonstrated on "Quote" tick data from the $/DM exchange rate (1993–1995).
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