# Spectral Dependence

arXiv: https://arxiv.org/abs/2103.17240 · HTML: https://mlsanity.com/paper/2103.17240/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis](https://mlsanity.com/paper/2505.07276/) (2025)
- [Topological Analysis for Detecting Anomalies (TADA) in Time Series](https://mlsanity.com/paper/2406.06168/) (2024)
- [Emergent Granger Causality in Neural Networks: Can Prediction Alone Reveal Structure?](https://mlsanity.com/paper/2506.20347/) (2025)
- [Robust Spectral Fuzzy Clustering of Multivariate Time Series with Applications to Electroencephalogram](https://mlsanity.com/paper/2506.22861/) (2025)
- [Canonical Tail Dependence for Soft Extremal Clustering of Multichannel Brain Signals](https://mlsanity.com/paper/2512.06435/) (2025)
- [Inference for High-Dimensional Sparse Spectral Precision Matrices](https://mlsanity.com/paper/2606.07986/) (2026)

## Abstract (arXiv)

This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence properties through these oscillatory activities.The unifying theme across the paper is to explore the strength of dependence and possible lead-lag dynamics through filtering. The proposed framework is capable of representing both linear and non-linear dependencies that could occur instantaneously or after some delay(lagged dependence). Examples for studying dependence between oscillations are illustrated through multichannel electroencephalograms. These examples emphasized that some of the most prominent frequency domain measures such as coherence, partial coherence,and dual-frequency coherence can be derived as special cases under this general framework.This paper also introduces related approaches for modeling dependence through phase-amplitude coupling and causality of (one-sided) filtered signals.