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Incorporating nonlinearity is paramount to predicting the future states of adynamical 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 tocapture the complexity. Here, we introduce a vector autoencoder nonlinearautoregression neural network (VANAR) capable of both automatic time seriesfeature extraction for its inputs and functional form estimation. We evaluateVANAR in three ways: first in terms of pure forecast accuracy, second in termsof detecting the correct causality between variables, and lastly in terms ofimpulse response where we model trajectories given external shocks. These testswere performed on a simulated nonlinear chaotic system and an empirical systemusing Philippine macroeconomic data. Results show that VANAR significantlyoutperforms VAR in the forecast and causality tests. VANAR has consistentlysuperior accuracy even over state of the art models such as SARIMA and TBATS.For the impulse response test, both models fail to predict the shockedtrajectories of the nonlinear chaotic system. VANAR was robust in its abilityto model a wide variety of dynamics, from chaotic, high noise, and low dataenvironments to macroeconomic systems.

Forecasting, Causality, and Impulse Response with Neural Vector Autoregressions