LASSO-ARIMA-BP Neural Network Combination Prediction Model and its Application to Exchange Rate Prediction

The ARIMA model is a popular way to forecast financial time series. However, many time series such as financial or biological time series often have nonlinear properties which cause in model errors during the evolutionary of fitting ARIMA models, and this results in significant prediction errors. To overcome this dilemma, a nonlinear autoregressive model is proposed which combines the method of LASSO, ARIMA, and BP neural network in the time-series modellings. Firstly, the LASSO model is used to reduce the dimensions of the input exogenous variables where the exchange rate is seen as endogenous variables, and the selected variables are those playing important roles, at the same time, the multicollinearity can also be eliminated. Secondly, based on the observing values of endogenous and exogenous variables, the BP neural networks with these selected variables are trained to obtain the nonlinear prediction models which are used to make predictions. Furthermore, in order to check whether there exist the correlations in the residual sequences, the white noise tests are proposed. If it fails, we use the ARIMA model to make further predictions to obtain more accurate predictions. Thirdly, the reciprocal variance methods are used to combine the results from the BP neural network and the ARIMA model, and the ideal predictive values are obtained. Finally, the proposed LASSO-ARIMA-BP neural network model are applied to predict the exchange rate. Comparing with other models such as random forest, ARIMA, and BP neural network using different evaluation metrics, it illustrates that the proposed combined model is more accurate in the exchange rate predictions.