Common functional principal components
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.
Year of publication: |
2006
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Authors: | Benko, Michal ; Härdle, Wolfgang Karl ; Kneip, Alois |
Publisher: |
Berlin : Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk |
Saved in:
freely available
Series: | SFB 649 Discussion Paper ; 2006,010 |
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Type of publication: | Book / Working Paper |
Type of publication (narrower categories): | Working Paper |
Language: | English |
Other identifiers: | 512461546 [GVK] hdl:10419/25093 [Handle] |
Source: |
Persistent link: https://www.econbiz.de/10010274114
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