Prediction of Hilbertian autoregressive processes : a Recurrent Neural Network approach
This work addresses prediction challenges in fields like finance and biology, but it is incremental as it applies existing neural network techniques to a known model.
The paper tackles the problem of predicting Hilbertian autoregressive processes by comparing a classical method based on estimating the autocorrelation operator with a neural network approach using Long Short-Term Memory networks, finding that the neural network method performs competitively in simulations and real datasets.
The autoregressive Hilbertian model (ARH) was introduced in the early 90's by Denis Bosq. It was the subject of a vast literature and gave birth to numerous extensions. The model generalizes the classical multidimensional autoregressive model, widely used in Time Series Analysis. It was successfully applied in numerous fields such as finance, industry, biology. We propose here to compare the classical prediction methodology based on the estimation of the autocorrelation operator with a neural network learning approach. The latter is based on a popular version of Recurrent Neural Networks : the Long Short Term Memory networks. The comparison is carried out through simulations and real datasets.