Inverse Cross-spectral Neural Networks for Multivariate Time Series
Abstract
CoVariance Neural Networks and their extensions have emerged as effective tools for processing multivariate data, deriving graph shift operators directly from second-order statistics. These architectures, however, are designed for independent and identically distributed observations and do not fully capture the joint structure of temporal and cross-variable dependencies in multivariate time series. In this work, we introduce Inverse Cross-Spectral Neural Networks (iCSNNs), a class of graph neural networks for stationary multivariate time series whose shift operators are the inverse cross-spectral density (iCSD) matrices. These operators encode frequency-specific conditional relationships among variables, exploiting the decomposition provided by the spectral representation theorem. Leveraging spectral smoothness, frequencies are grouped into bands sharing a single iCSD operator, yielding a compact parametrisation that retains the frequency-dependent structure of the process. We further propose a joint learning procedure to estimate both the Fourier-domain dependence structure and the iCSNN parameters, adapting the iCSD operators to the downstream task. When tested on synthetic data, iCSNN outperforms baselines from different methodological families.
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BibTeX
@misc{marinucci2026inverse,
title = {{Inverse Cross-spectral Neural Networks for Multivariate Time Series}},
author = {Lorenzo Marinucci and Leonardo Di Nino and Gabriele D'Acunto and Paolo Di Lorenzo and Sergio Barbarossa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06630},
eprint = {2610.06630},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06630},
}
RIS
TY - UNPB
TI - Inverse Cross-spectral Neural Networks for Multivariate Time Series
AU - Lorenzo Marinucci
AU - Leonardo Di Nino
AU - Gabriele D'Acunto
AU - Paolo Di Lorenzo
AU - Sergio Barbarossa
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06630
UR - https://arxiv.org/abs/2610.06630
AB - CoVariance Neural Networks and their extensions have emerged as effective tools for processing multivariate data, deriving graph shift operators directly from second-order statistics. These architectures, however, are designed for independent and identically distributed observations and do not fully capture the joint structure of temporal and cross-variable dependencies in multivariate time series. In this work, we introduce Inverse Cross-Spectral Neural Networks (iCSNNs), a class of graph neural networks for stationary multivariate time series whose shift operators are the inverse cross-spectral density (iCSD) matrices. These operators encode frequency-specific conditional relationships among variables, exploiting the decomposition provided by the spectral representation theorem. Leveraging spectral smoothness, frequencies are grouped into bands sharing a single iCSD operator, yielding a compact parametrisation that retains the frequency-dependent structure of the process. We further propose a joint learning procedure to estimate both the Fourier-domain dependence structure and the iCSNN parameters, adapting the iCSD operators to the downstream task. When tested on synthetic data, iCSNN outperforms baselines from different methodological families.
ER -