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

摘要： 分别使用基于滑动窗口的VLRBP神经网络模型和基于C-C相空间重构的VLRBP神经网络模型及ARIMA-GARCH模型对欧元汇率时间序列建模和预测，通过比较发现基于C-C相空间重构的VLRBP神经网络对于含有大量非线性成分的欧元汇率时间序列的预测比较准确。同时，为了提高基于滑动窗口的VLRBP网络的泛化性能，提出在训练VLRBP神经网络时应用浴盆曲线方法选取隐层神经元个数和滑动窗口尺寸。

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