Prediction of Hilbertian autoregressive processes : a Recurrent Neural Network approach

TL;DR

This paper compares traditional autocorrelation-based prediction methods for Hilbertian autoregressive processes with a neural network approach using LSTM networks, through simulations and real data analysis.

Contribution

It introduces a neural network-based prediction method for Hilbertian autoregressive processes and compares its performance with classical methods.

Findings

Neural network approach performs competitively with traditional methods.

LSTM networks effectively model Hilbertian autoregressive processes.

Simulation and real data results demonstrate the potential of neural networks in this context.

Abstract

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.