Kernel Based Goodness-of-Fit Tests for Copulas with Fixed Smoothing Parameters
AbstractWe study a test statistic on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a U-statistic of order 4 with degeneracy of order 3. For practical implementation we suggest to compute the critical values through a semiparametric bootstrap. Monte Carlo results show that the bootstrap procedure performs well in small samples. In particular size and power are less sensitive to smoothing parameter choice than they are under the asymptotic approximation obtained for a vanishing bandwidth.
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Bibliographic InfoPaper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp145.
Date of creation: May 2005
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Nonparametric; Copula density; Goodness-of-fit test; U-statistic.;
Other versions of this item:
- Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 533-543, March.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- D18 - Microeconomics - - Household Behavior - - - Consumer Protection
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
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- NEP-ALL-2005-06-05 (All new papers)
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