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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Cite this article
APA 7
Marinucci, L., Nino, L. D., D'Acunto, G., Lorenzo, P. D., & Barbarossa, S. (2026). Inverse Cross-spectral Neural Networks for Multivariate Time Series. https://omanscience.com/en/articles/inverse-cross-spectral-neural-networks-for-multivariate-time-series
MLA 9
Marinucci, Lorenzo, et al. "Inverse Cross-spectral Neural Networks for Multivariate Time Series." https://omanscience.com/en/articles/inverse-cross-spectral-neural-networks-for-multivariate-time-series.
Chicago (author–date)
Marinucci, Lorenzo, Leonardo Di Nino, Gabriele D'Acunto, Paolo Di Lorenzo, and Sergio Barbarossa. 2026. "Inverse Cross-spectral Neural Networks for Multivariate Time Series." https://omanscience.com/en/articles/inverse-cross-spectral-neural-networks-for-multivariate-time-series.
Harvard
Marinucci, L., Nino, L. D., D'Acunto, G., Lorenzo, P. D. and Barbarossa, S. (2026) 'Inverse Cross-spectral Neural Networks for Multivariate Time Series', Available at: https://omanscience.com/en/articles/inverse-cross-spectral-neural-networks-for-multivariate-time-series.
Vancouver
Marinucci L, Nino LD, D'Acunto G, Lorenzo PD, Barbarossa S. Inverse Cross-spectral Neural Networks for Multivariate Time Series. https://omanscience.com/en/articles/inverse-cross-spectral-neural-networks-for-multivariate-time-series
IEEE
L. Marinucci, L. D. Nino, G. D'Acunto, P. D. Lorenzo, and S. Barbarossa, "Inverse Cross-spectral Neural Networks for Multivariate Time Series," https://omanscience.com/en/articles/inverse-cross-spectral-neural-networks-for-multivariate-time-series.