Semiparametric ARX Neural Network Models with an Application to Forecasting In°ation¤

In this paper we examine semiparametric nonlinear autoregressive models with ex-ogenous variables (NLARX) via three classes of arti¯cial neural networks: the ¯rst 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 ¯-mixing data. As an empirical application, we com-pare the forecasting performance of linear and semiparametric NLARX models of U.S. in°ation. We ¯nd 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 in°ation and the GDP gap is best in terms of both forecast mean squared error and forecast mean absolute deviation error