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

In this paper, we examine semiparametric nonlinear autoregressive models wi th exogenous variables (NLARX) via three classes of artificial neural netwo rks: the first one uses smooth sigmoid activation functions; the second one uses radial basis activation functions; and the third one uses ridgelet ac tivation functions, We provide root mean squared error convergence rates fo r these ANN estimators of the conditional mean and median functions with st ationary beta -mixing data. As an empirical application, we compare the for ecasting performance of linear and semiparametric NLARX models of U.S. infl ation. 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 histor ical inflation and the GDP gap is best in terms of both forecast mean squar ed error and forecast mean absolute deviation error.