Impulse Response and Granger Causality in Dynamical Systems with Autoencoder Nonlinear Vector Autoregressions
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Sometimes knowing the future given the present is not enough. For sound policy making, predicting possible futures given different user defined scenarios can be more important. However, the workhorse for causality detection and impulse response, the Vector Autoregression (VAR), assumes linearity and has produced poor forecasts (Reis, 2018). Here, we introduce a vector autoencoder nonlinear autoregression neural network (VANAR) capable of both automatic time series feature extraction for its inputs and automatic functional form estimation. We compare the performance of VANAR and VAR across three tests: (1) forecasting skill, measured as n-step ahead forecast accuracy, (2) correct detection of Granger Causality between variables, and (3) impulse response tests on modeled trajectories subject to external shocks. These tests were performed on datasets with different underlying dynamics: a simulated nonlinear chaotic system, a simulated linear system, and an empirical system using Philippine macroeconomic data. Results show that VANAR significantly outperforms VAR in terms of the forecast and causality tests especially for the nonlinear and empirical macroeconomic systems. For the impulse response test, VANAR outperforms VAR in the linear system but 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 complex macroeconomic systems, thus illustrating its potential usefulness in modeling more real world dynamical systems.
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