Empirical comparison between multiple time series and functional data analysis

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Vega-Cadillo, Claudio Andres
Embargoed Until
Acuña-Fernández, Edgar
College of Arts and Sciences - Sciences
Department of Mathematics
Degree Level
Despite Functional data analysis being a competitor of time series analysis, it has been found that in the last 15 years it has not been requested as much as multiple time series by the scientific community. The main goal of this thesis is to study the similarities and differences between multiple time series analysis and functional data analysis. This was done by comparing the results of four main tasks: "Principal Component Analysis", "Outlier Detection", "Cluster Analysis" and "Supervised Classification" for both approaches in five real world datasets. After the experiments, it was found that for detecting outliers and principal components the Functional Data approach was superior. For clustering and classification, the Multiple Time Series approach performed slightly better, even though the methods were slower. Finally, Functional Data may not be as popular as Multiple time series, but it has been showed that it gives better results in terms on general analysis for one dimensional data.

A pesar de que el análisis funcional de datos es un competidor del análisis de series de tiempo, se ha encontrado que en los últimos 15 años no ha sido solicitado tanto como series de tiempo múltiples por la comunidad científica. El objetivo principal de esta tesis es estudiar las similitudes y diferencias entre el análisis de múltiples series de tiempo y el análisis de datos funcionales. Esto se hizo comparando los resultados de cuatro tareas principales: "Análisis de componentes principales", "Detección de valores atípicos", "Análisis de conglomerados" y "Clasificación supervisada" para ambos enfoques en cinco conjuntos de datos del mundo real. Después de los experimentos, se encontró que, para detectar valores atípicos y componentes principales, el enfoque de datos funcionales era superior. Para el agrupamiento y la clasificación, el enfoque de Series de Tiempo Múltiple funcionó ligeramente mejor, aunque los métodos fueron más lentos. Por último, es posible que los datos funcionales no sean tan populares como las series temporales múltiples, pero se ha demostrado que ofrece mejores resultados en términos de análisis general para datos unidimensionales.
Functional data analysis,
Multiple time series,
Cluster analysis,
Supervised classification,
Outlier detection
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Vega-Cadillo, C. A. (2021). Empirical comparison between multiple time series and functional data analysis [Thesis]. Retrieved from