A Study of the Colombian Stock Market with Multivariate Functional Data Analysis (FDA)

Deivis Rodríguez Cuadro, Sonia Pérez-Plaza (), Antonia Castaño-Martínez and Fernando Fernández-Palacín
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Deivis Rodríguez Cuadro: Departamento de Matemáticas, Universidad del Atlántico, Puerto Colombia 081001, Colombia
Sonia Pérez-Plaza: Department of Statistics and Operations Research, University of Cádiz, 11510 Puerto Real, Spain
Antonia Castaño-Martínez: Department of Statistics and Operations Research, University of Cádiz, 11510 Puerto Real, Spain
Fernando Fernández-Palacín: Department of Statistics and Operations Research, University of Cádiz, 11510 Puerto Real, Spain

Mathematics, 2025, vol. 13, issue 5, 1-18

Abstract: In this work, Functional Data Analysis (FDA) is used to detect behavioral patterns in the Bolsa de Valores de Colombia (BVC) in reaction to the global crises caused by COVID-19 and the war in Ukraine. The oil price fluctuation curve is considered a covariate. The FDA’s distinctive ability is to represent stock values as smooth curves that evolve over time and provide new insights into the dynamics of the BVC. The methodology makes use of functional multivariate techniques applied to the smoothed curves of the closing prices of the main stocks of the BVC. The results show that the correlations of the oil curve with the average market curve change from almost null or low in the global period to extremely significant in time windows immediately after the beginnings of COVID-19 and the war in Ukraine, respectively. On the other hand, the velocity curves, which are used to evaluate the stock market volatility, show a pattern of synchronization of companies in the crisis periods. Furthermore, in these crisis periods, the companies in BVC showed a high synchronization with the Brent crude oil price. In conclusion, this work shows the usefulness of the FDA as a complement to time series analysis in the study of stock markets. The results of this research could be of interest to academic researchers, financial analysts, or institutions.

Keywords: functional data analysis; stock market; volatility; functional principal component analysis; k-means clustering (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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