Semiparametric ARX neural-network models with an application to forecasting inflation

We examine semiparametric nonlinear autoregressive models with exogenous variables (NLARX) via three classes of artificial neural networks: the first one uses smooth sigmoid activation functions; the second one uses radial basis activation functions; and the third one uses ridgelet activation functions. We provide root mean squared error convergence rates for these ANN estimators of the conditional mean and median functions with stationary beta-mixing data. As an empirical application, we compare the forecasting performance of linear and semiparametric NLARX models of US inflation. We find that all of our semiparametric models outperform a benchmark linear model based on various forecast performance measures. In addition, a semiparametric ridgelet NLARX model which includes various lags of historical inflation and the GDP gap is best in terms of both forecast mean squared error and forecast mean absolute deviation error.