关键词: 时间序列, VLRBP神经网络, 相空间重构, ARIMA-GARCH模型, 浴盆曲线

Abstract: It builds a sliding window neural networks model，a neural networks model which is based on phase space reconstruction and an ARIMA-GARCH model，and then the euro foreign exchange rate is forecasted by using the three models.The result shows that the VLRBP neural networks which is based on C-C phase space reconstruction produces better porformance than the other methods in forecasting the euro foreign exchange rate which has a great amount nonlinear components.To improve the generalization performance of the sliding window VLRBP neural networks，it presents a bathtub curve method when searching the size of the hidden neuron and the sliding window of the VLRBP neural networks.

Key words: time series, Variable Learning Rate Back Propagation（VLRBP） neural networks, phase space reconstruction, ARIMA-GARCH model, bathtub curve