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

Area of Science:

• Econometrics
• Machine Learning
• Time Series Analysis

Background:

• Nonlinear autoregressive models with exogenous variables (NLARX) are crucial for time series forecasting.
• Traditional linear models may not capture complex dynamics in economic data.
• Artificial neural networks (ANNs) offer flexible function approximation capabilities.

Purpose of the Study:

• To investigate semiparametric NLARX models using three distinct ANN architectures.
• To establish theoretical convergence rates for ANN estimators.
• To compare the empirical forecasting performance of these models against a linear benchmark for US inflation.

Main Methods:

• Utilizing three classes of ANNs: smooth sigmoid, radial basis, and ridgelet activation functions.
• Deriving root mean squared error (RMSE) convergence rates for stationary beta-mixing data.
• Empirically applying the models to forecast US inflation, including lags of historical inflation and the GDP gap.

Main Results:

• All proposed semiparametric NLARX models demonstrated superior forecasting performance compared to the benchmark linear model.
• The semiparametric ridgelet NLARX model achieved the best performance across key forecast accuracy metrics.
• The models provide reliable estimates for conditional mean and median functions.

Conclusions:

• Semiparametric NLARX models implemented with ANNs are effective for improving inflation forecasts.
• Ridgelet-based ANNs show particular promise for capturing complex economic time series patterns.
• The findings support the use of advanced machine learning techniques in econometric modeling.