Reservoir kernels and Volterra series

Item Type Monograph (Working Paper)
Abstract A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir functional associated with a state-space representation of the Volterra series expansion available for any analytic fading memory filter. It is hence called the Volterra reservoir kernel. Even though the statespace representation and the corresponding reservoir feature map are defined on an infinite-dimensional tensor algebra space, the kernel map is characterized by explicit recursions that are readily computable for specific data sets when employed in estimation problems using the representer theorem. We showcase the performance of the Volterra reservoir kernel in a popular data science application in relation to bitcoin price prediction.
Authors Gonon, Lukas; Grigoryeva, Lyudmila & Ortega Lahuerta, Juan-Pablo
Language English
Subjects finance
HSG Classification contribution to scientific community
HSG Profile Area SEPS - Quantitative Economic Methods
Date 30 December 2022
Depositing User Barbara Langenegger
Date Deposited 01 Dec 2022 08:53
Last Modified 28 Feb 2023 12:41


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Gonon, Lukas; Grigoryeva, Lyudmila & Ortega Lahuerta, Juan-Pablo: Reservoir kernels and Volterra series. , 2022,

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