Understanding fluctuations through Multivariate Circulant Singular Spectrum Analysis

TL;DR

This paper introduces Multivariate Circulant Singular Spectrum Analysis (M-CiSSA), a non-parametric method for analyzing complex fluctuations in multivariate time series, capable of disentangling sources of variation and phase relationships across frequencies.

Contribution

The paper presents a novel, non-parametric framework for multivariate fluctuation analysis that identifies common sources of variation without fitting a factor model, applicable to nonlinear and modulated series.

Findings

Successfully applied to synthetic data with modulated signals

Effectively analyzed energy price co-movements at multiple frequencies

Proven uniqueness theorem for source identification

Abstract

We introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) to provide a comprehensive framework to analyze fluctuations, extracting the underlying components of a set of time series, disentangling their sources of variation and assessing their relative phase or cyclical position at each frequency. Our novel method is non-parametric and can be applied to series out of phase, highly nonlinear and modulated both in frequency and amplitude. We prove a uniqueness theorem that in the case of common information and without the need of fitting a factor model, allows us to identify common sources of variation. This technique can be quite useful in several fields such as climatology, biometrics, engineering or economics among others. We show the performance of M-CiSSA through a synthetic example of latent signals modulated both in amplitude and frequency and through the real data analysis of energy prices to understand the main drivers and co-movements of primary energy commodity prices at various frequencies that are key to assess energy policy at different time horizons.