A neural network method for nonlinear time series analysis

This paper is concerned with approximating nonlinear time series by an artificial neural network based on radial basis functions. A new data-driven modelling strategy is suggested for the adaptive framework by combining the statistical techniques of forward selection, cross validation and information criterion. The proposed method is fast and simple to implement while avoiding some typical difficulties such as estimation and computation of nonlinear econometric models. Two applications are provided to illustrate the benefits of using the neural network method in time series analysis. First, the proposed modelling method is applied to a neural network test for neglected nonlinearity in conditional mean of univariate time series. A simulation study is carried out to show how the size of the test is improved in finite samples. Further, the new test is compared with alternative popular tests to demonstrate its superior power performance using a variety of nonlinear time series models. Second, the proposed method is applied to obtain a nonlinear forecasting model for daily S&P 500 returns. Forecast accuracy is compared with that of a linear model and other neural network models used in the literature.