Resource title

Common functional principal components

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Resource description

Functional principal component analysis (FPCA) based on the Karhunen-Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the logreturns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. Firstly we present a new method for estimation of functional principal components from discrete noisy data. Next we present the two sample inference for FPCA and develop two sample theory. We propose bootstrap tests for testing the equality of eigenvalues, eigenfunctions, and mean functions of two functional samples, illustrate the test-properties by simulation study and apply the method to the IV analysis.

Resource author

Michal Benko, Wolfgang Karl Härdle, Alois Kneip

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Resource publish date

Resource language

eng

Resource content type

text/html

Resource resource URL

http://hdl.handle.net/10419/25093

Resource license

Adapt according to the presented license agreement and reference the original author.