Modeling cyclostationarity in time series using ASCA

TL;DR

This paper introduces a unified pipeline using ASCA to analyze cyclostationary time series, enhancing interpretability and multiscale modeling of periodic patterns in observational data.

Contribution

It extends ASCA for time series analysis, enabling multiscale cyclostationary modeling with improved interpretability and handling of autocorrelation in observational data.

Findings

ASCA better separates variability across factors than ANOVA in unbalanced designs.

The methodology effectively analyzes real-world data like lake temperatures and pollen trends.

ASCA provides enhanced interpretability through visualization in PCA.

Abstract

Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily, weekly or yearly cycles. In this context, statistical inference is essential to distinguish genuine underlying effects from random variability. While tools like Analysis of Variance (ANOVA) provide such inference, they often lack interpretability and struggle with the complexities of multivariate data. To address these limitations, we propose a unified pipeline for the exploratory analysis of cyclostationary times series using ANOVA Simultaneous Component Analysis (ASCA). ASCA is an extension of ANOVA that is able to work in both univariate and multivariate cases. Combining inference with the visualization capabilities of Principal Component Analysis (PCA), ASCA provides powerful options for interpretability. ASCA's capabilities have been well-established in the analysis of experimental data, but they remain largely unexplored for observational data like time series. Our workflow introduces an algorithmic approach to modeling time-dependent data using ASCA, enabling control over multiple cyclostationary time scales while also accounting for the specific challenges of this type of data, such as autocorrelation. Furthermore, we observed that ASCA provides a better separation of variability across factors than ANOVA in unbalanced designs due to its multivariate nature. We demonstrate the efficacy of this methodology through two real-world case studies: water temperature trends in mountain lakes in Sierra Nevada, Spain, and airborne pollen trends over 30 years recorded in the city of Granada, Spain.