Forecasting, Causality, and Impulse Response with Neural Vector Autoregressions

Incorporating nonlinearity is paramount to predicting the future states of a dynamical system, its response to shocks, and its underlying causal network. However, most existing methods for causality detection and impulse response, such as Vector Autoregression (VAR), assume linearity and are thus unable to capture the complexity. Here, we introduce a vector autoencoder nonlinear autoregression neural network (VANAR) capable of both automatic time series feature extraction for its inputs and functional form estimation. We evaluate VANAR in three ways: first in terms of pure forecast accuracy, second in terms of detecting the correct causality between variables, and lastly in terms of impulse response where we model trajectories given external shocks. These tests were performed on a simulated nonlinear chaotic system and an empirical system using Philippine macroeconomic data. Results show that VANAR significantly outperforms VAR in the forecast and causality tests. VANAR has consistently superior accuracy even over state of the art models such as SARIMA and TBATS. For the impulse response test, both models fail to predict the shocked trajectories of the nonlinear chaotic system. VANAR was robust in its ability to model a wide variety of dynamics, from chaotic, high noise, and low data environments to macroeconomic systems.