  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.
