A Neural Learning Approach for a Data-Driven Nonlinear Error Correction Model

A nonlinear error correction model (ECM) is developed to fit nonlinear relationships between the nonstationary time series in a cointegration relationship. Different from the previous parametric methods, this paper constructs a hybrid neural network to learn the nonlinear error correction model by combining a linear recurrent neural network with a multilayer BP network. The network learning algorithm is given by using the gradient descent method and error back propagation. Based on the principle of data-driven, all network parameters can be obtained through the network learning and training. The daily data of gold price and the US dollar index in 2021 were used to verify this proposed nonlinear ECM neural learning method and the results were compared by the likelihood ratio Chi-square test. Simulation results show that the proposed data-driven nonlinear error correction neural learning method can improve goodness of fit statistical significantly of complex nonlinear relationship between time series.