Stochastic Nonlinear Time Series Forecasting Using Time-Delay Reservoir Computers: Performance and Universality
International audience; 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 …
Random walks and random numbers from supercontinuum generation
International audience; We report a numerical study showing how the random intensity and phase fluctuations across the bandwidth of a broadband optical supercontinuum can be interpreted in terms of the random processes of random walks and L´evy flights. We also describe how the intensity fluctuations can be applied to physical random number generation. We conclude that the optical supercontinuum provides a highly versatile means of studying and generating a wide class of random processes at optical wavelengths.