Bivariate Functional Archetypoid Analysis: An Application to Financial Time Series

Abstract

Archetype Analysis (AA) is a statistical technique that describes individuals of a sample as a convex combination of certain number of elements called Archetypes, which in turn, are convex combinations of the individuals in the sample. For it's part, Archetypoid Analysis (ADA) tries to represent each individual as a convex combination of a certain number of extreme subjects called Archetypoids. It is possible to apply these techniques to functional data applying a basis expansion function and performing AA or ADA to the weighted coefficients in the basis.This document presents an application of Functional Archetypoids Analysis (FADA) to financial time series. The starting time series consists of daily equity prices of the SP500 stocks. From it, measures of volatility and profitability are generated in order to characterize listed companies. These variables are converted into functional data through a Fourier basis expansion function and bivariate FADA is applied. By representing subjects through extreme cases, this analysis facilitates the understanding of both the composition and the relationships between listed companies. Finally, a cluster methodology based on a similarity parameter is presented. Therefore, the suitability of this technique for this kind of time series is shown, as well as the robustness of the conclusions drawn.

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

“…As both functions are measured in non-compatible units, each functional variable is standardized before analysis by standardizing the coefficients in the basis as explained by Epifanio (2016). This data set was analyzed in a non-robust way by Moliner and Epifanio (2018), using the Fourier basis. Table 5 shows the companies obtained as archetypoids for different k values.…”

Classifying top economists using archetypoid analysis

“…Archetypal analysis has aroused the interest of researchers working in various fields, such as astrophysics (Chan et al 2003), machine learning (Mørup and Hansen 2012;Seth and Eugster 2016), and sports (Seth and Eugster 2016). The same applies for the archetypoid analysis, which was used for the evaluation within fields such as sports (Vinué and Epifanio 2017) and the financial stock market (Moliner and Epifanio 2018).…”

Classifying Top Economists Using Archetypoid Analysis

“…Archetypal analysis has aroused the interest of researchers working in various fields, such as astrophysics (Chan et al 2003), climate (Steinschneider and Lall 2015), machine learning (Morup andHansen 2012, Seth andEugster 2016), neuroscience (Hinrich et al 2016), navigation (Feld et al 2015) and sports (Seth and Eugster 2016). The same applies for the archetypoid analysis, which was used for the evaluation within fields such as astrophysics (Sun et al 2017), sports (Vinué and Epifanio 2017) and the financial stock market (Moliner and Epifanio 2018).…”