A study of functional data analysis on yield curves

We introduce functional data and a basis function systems to represent it. The B-splinebasis system is explored further as we will apply it in our application. We explore principalcomponent analysis and functional principal component analysis. We apply functional prin-cipal component analysis on yield curves of the United States. We validate that functionalprincipal component analysis gives similar results as principal component analysis. We createtwo different scenarios namely a crisis scenario and a growth scenario and apply functionalprincipal component analysis on them. Here we see that in a extreme scenario the impactof the second and the third principal component both significantly increase. In the end weintroduce forecasting of functional time series using a weighted functional principal componentregression. We apply a simplified model of this forecast on the yield curves.

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A study of functional data analysis on yield curves