An Improved BP Algorithm with Adaptive Smoothing Momentum Terms for Foreign Exchange Rates Prediction

Back-propagation neural network (BPNN) is one of the most popular neural networks which have been widely applied to many fields such as prediction and pattern recognition due to their strong capability to approximate any arbitrary function arbitrarily well and to provide flexible nonlinear mapping between inputs and outputs (Hornik et al., 1989; White, 1990). The basic learning rule of BPNN is based on the gradient descent optimization method and the chain rule (Widrow and Lehr, 1990). However, some typical drawbacks of the BPNN learning rule based on the gradient descent method are its slowness and its frequent confinement to local minima and over-fitting (Yu, 1992; Lawrence et al., 1997; Yu et al., 2006a). For these reasons, some global optimization algorithms, such as genetic algorithm (GA) (Jain et al., 1996) and simulated annealing (SA) (Karaboga and Pham, 2000), are proposed for escaping local minima.

In this chapter, we propose an improved BPNN learning algorithm with adaptive smoothing momentum. In this new algorithm, adaptive smoothing technique is used to adjust the momentum of weight updating formula automatically by tracking error signals in terms of “3

σ

limits theory”. For illustration and verification purposes, the proposed BPNN learning algorithm is applied to foreign exchange rates prediction.

The rest of this chapter is organized as follows. In Section 6.2, an improved BPNN learning algorithm with adaptive smoothing momentum terms is proposed in detail. In order to verify the effectiveness of the proposed algorithms, an exchange rate index prediction experiment of tradingweighted US dollar against currencies of major US trading partners is conducted and the corresponding results are reported in Section 6.3. In addition, Section 6.4 compares the proposed model with the two similar single neural network models proposed by Chapters 4 and 5. Finally, some concluding remarks are drawn in Section 6.5.