Functional Data Analysis: Theory and Applications to Financial Time Series

BSc Thesis (Statistics) — University of Extremadura, 2025

This thesis was proposed and supervised by Julián Ramajo Hernández, full professor of economics at the University of Extremadura. Functional data analysis (FDA) treats each observation not as a number or a vector but as a curve, and the thesis builds the machinery to work with such data: representing discrete observations as smooth functions through basis expansions and smoothing, detecting outliers, and reducing dimensionality via functional principal components. On this foundation it develops unsupervised and supervised methods: clustering of curves and functional regression in its three forms (scalar-on-function, function-on-scalar and function-on-function), both linear and nonlinear. The final chapter applies these tools to 655 European bond yield curves from the ECB spanning the 2006–2009 financial crisis: after smoothing and clustering the curves, a scalar-on-function regression explains the daily closing value of the IBEX35 from bond yields, first by ordinary least squares and then with penalized estimation to reduce overfitting. The analysis was carried out in R.