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.

Keywords: Reservoir computing, echo state networks, neural computing, time-delay reservoir, time series forecasting, universality, VEC-GARCH model, volatility forecasting, realized volatility, parallel reservoir computing

JEL Classification: C45, C53, C63