Deep Learning Accelerates Spectral Density Estimation for Functional Time Series

This paper presents a novel deep learning approach to address the computational bottleneck in spectral density estimation for functional time series, particularly those defined on large domains. By circumventing the need to compute large autocovariance kernels, the proposed method offers a significant speedup and enables analysis of datasets previously intractable. The application to fMRI images demonstrates the practical relevance and potential impact of this technique.