Common Functional Principal Components
AbstractFunctional principal component analysis (FPCA) based on the Karhunen-Lo`eve 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.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-010.
Length: 35 pages
Date of creation: Jan 2006
Date of revision:
Functional Principal Components; Nonparametric Regression; Bootstrap; Two Sample Problem;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- G19 - Financial Economics - - General Financial Markets - - - Other
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