VECM + Neural Network: A semiparametric model of cointegrated data

In this article, I explore a method of nonlinear time series estimation, which combines elements of an artifical neural network (NN) and a vector error correction model (VECM). The aim is to develop a semiparametric VECM, which is capable of modelling nonlinear short-run behaviour of an unknown functional form, while retaining the ability to draw inferential conclusions about the long-run equilibrium behaviour of the data. This approach is particularly useful for data periods including financial crises, multiple regimes and other nonlinear characteristics, which are difficult to handle in a purely linear setting.

The artificial neural network (NN) is a powerful tool for modeling nonlinear empirical relationships. Various authors demonstrate the so-called Universal Approximation Theorem (see for instance Hornik (1991)), proving that single-layer neural networks can approximate any arbitrary function. This makes it an elegant alternative to other nonlinear approaches — particularly, when the functional form of the data-generating process (DGP) is unknown.

Using artificial neural networks to capture nonlinearities in time series data has received a fair amount of attention in the past. Autoregressive neural network (AR-NN) models are well established and have been applied broadly (see Enders (2015)). Various studies compare the performance of multivariate neural network (VAR-NN) models against standard vector autoregression models (see Wutsqa, Subanar, and Sujuti (2006) and Aydin and Cavdar (2015)). Generally, NN-based models exhibit superior performance for prediction purposes, while this comes at the expense of model inference, given the “black-box” nature of the NN component. As always, there is no free lunch in econometrics.