An artificial neural network for mixed frequency data

In the big data area, a large number of variables are observed at mixed frequencies. How to explore the potential nonlinear pattern hidden in raw mixed frequency data without information loss is a challenging work. To this end, we develop a simple artificial neural network (ANN) model for mixed frequency data through introducing a mixed data sampling (MIDAS) or unrestricted MIDAS (U-MIDAS) approach into the ANNs framework, and construct the ANN-(U-)MIDAS model. It enables us to use raw mixed frequency data as inputs directly, and does not involve latent processes for preprocessing the data before feeding them into the neural network. Based on the backpropagation and chain rule, we derive the gradient vector and provide a solution procedure with the standard gradient based nonlinear optimization algorithm. We conduct extensive Monte Carlo simulations and a real-world application to illustrate the efficacy of the ANN-(U-)MIDAS, and then compare its decent performance with those of other competing models in terms of goodness-of-fit and predictive ability. The numerical results show that the hybrid ANN-(U-)MIDAS model is an efficient tool to handle nonlinear mixed frequency data and has a broad application prospect in the field of expert and intelligent systems.