Robust multivariate and functional archetypal analysis with application to financial time series analysis

TL;DR

This paper introduces a robust archetypal analysis method for multivariate and functional data, effectively handling outliers and enabling non-experts to interpret complex financial time series through new visualization techniques.

Contribution

A novel robust archetypal analysis approach using M-estimators for multivariate and functional data, with applications to financial time series and improved interpretability.

Findings

Robust method outperforms previous approaches in simulations.

Effective visualization aids non-expert understanding.

Application to S&P 500 data reveals meaningful archetypes.

Abstract

Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the analysis very sensitive to outliers. A robust methodology by means of M-estimators for classical multivariate and functional data is proposed. This unsupervised methodology allows complex data to be understood even by non-experts. The performance of the new procedure is assessed in a simulation study, where a comparison with a previous methodology for the multivariate case is also carried out, and our proposal obtains favorable results. Finally, robust bivariate functional archetypoid analysis is applied to a set of companies in the S\&P 500 described by two time series of stock quotes. A new graphic representation is also proposed to visualize the results. The analysis shows how the information can be easily interpreted and how even non-experts can gain a qualitative understanding of the data.