Nonlinear time series forecast using the artificial neural network and the local linear regression combined with dimensionality reduction techniques

This paper gives a detailed guide to building a forecasting method when high-dimensional predictors and possible nonlinear issues exist. From the predictors, a certain number of factors are extracted which will form predictive indices using the sliced inverse regression. This paper considers mainly two models that can be applied in nonlinear time series forecast: the artificial neural network (ANN) and the local linear regression (LLR). The paper describes a detailed procedure for building and training ANNs customized for time series forecast that uses the aforementioned dimension reduction techniques. In the simulation studies, by various evaluation criteria we examine the in-sample and out-of-sample performance of the ANNs and LLRs, which will also be compared to the conventional ordinary least squares (OLS). We find that when nonlinearity, such as interaction between factors, exists, the ANNs and LLRs perform superior to the OLS while the OLS shows the best performance in presence of the linearity. In the empirical application, the ANN and LLR also show superior forecasting performance compared to the OLS.