title: Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.
abstract: Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs.
authors.affiliation: Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, UFR des Sciences et Techniques. 16, route de Gray. F-25030 Besançon Cedex, France. Electronic address: Lyudmyla.Grygoryeva@univ-fcomte.fr.
authors.forename: Lyudmila
authors.initials: L
authors.lastname: Grigoryeva
authors.affiliation: Cegos Deployment. 11 rue Denis Papin. F-25000 Besançon, France. Electronic address: jhenriques@deployment.org.
authors.forename: Julie
authors.initials: J
authors.lastname: Henriques
authors.affiliation: UMR CNRS FEMTO-ST 6174/Optics Department, Université de Franche-Comté, UFR des Sciences et Techniques. 16, route de Gray. F-25030 Besançon Cedex, France. Electronic address: Laurent.Larger@univ-fcomte.fr.
authors.forename: Laurent
authors.initials: L
authors.lastname: Larger
authors.affiliation: Centre National de la Recherche Scientifique, Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, UFR des Sciences et Techniques. 16, route de Gray. F-25030 Besançon Cedex, France. Electronic address: Juan-Pablo.Ortega@univ-fcomte.fr.
authors.forename: Juan-Pablo
authors.initials: JP
authors.lastname: Ortega
mesh_terms: D001185:Artificial Intelligence; D003195:Computer Communication Networks / Q000295:instrumentation*; D003201:Computers; D003627:Data Interpretation, Statistical; D005544:Forecasting / Q000379:methods*; D006801:Humans; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D013269:Stochastic Processes; D013997:Time Factors
keywords: Echo state networks; Neural computing; Parallel reservoir computing; Realized volatility; Reservoir computing; Time series forecasting; Time-delay reservoir; Universality; VEC-GARCH model; Volatility forecasting