DeepTVAR: Deep learning for a time-varying VAR model with extension to integrated VAR

This paper proposes a new approach called DeepTVAR that employs a deep learning methodology for vector autoregressive (VAR) modeling and prediction with time-varying parameters. By optimizing the VAR parameters with a long short-term memory (LSTM) network, we retain the Markovian dependence for prediction purposes and make full use of the recurrent structure and powerful learning ability of the LSTM. To ensure the stability of the model, we enforce the causality condition on the autoregressive coefficients using the Ansley–Kohn transform. We provide a simulation study of the estimation ability using realistic curves generated from data. The model is extended to integrated VAR with time-varying parameters, and we compare its forecasting performance with existing methods when applied to energy price data.