Deep Impulse Response Functions for Macroeconomic Dynamics: A Hybrid LSTM-Wavelet Approach Compared to an ANN-Wavelet and VECM Models

This study presents a novel hybrid framework that integrated Long Short-Term Memory (LSTM) networks with Daubechies wavelet transforms to estimate Deep Impulse Response Functions (DIRF) for monthly macroeconomic time series, across five economies: Brazil, Egypt, Indonesia, United States, and the United Kingdom. Eight key variables, yield curve latent factors (LEVEL, SLOPE, CURVATURE), foreign exchange rates, equity indices, central bank policy rates, GDP growth rates, and inflation rates, were modeled using the proposed LSTM-Wavelet approach, and were compared against an ANN-Wavelet hybrid, and a traditional Vector Error Correction Model (VECM). The LSTM-Wavelet model achieved a superior overall median R2, outperforming the ANN-Wavelet and VECM. The approach excelled in capturing nonlinear dynamics and temporal dependencies for variables such as equity indices, policy rates, GDP, and inflation. Db4 was superior for capturing short and medium-term patterns in macroeconomic variables like GDP, EQUITY, and FX, cause its shorter filter and moderate smoothing excelled at isolating cyclical patterns in noisy, volatile data. Cumulative DIRFs revealed consistent cross variable dynamics e.g., yield curve shocks propagated to equity, FX, policy rates, GDP, and inflation, in line with economic theory. These findings underscored the hybrid model’s ability to capture non-linearity, multiscale interactions in macroeconomic data, offering valuable insights for forecasting and policy analysis.