Goodness-of-Fit Tests for Symmetric Stable Distributions - Empirical Characteristic Function Approach

Muneya Matsui and Akimichi Takemura
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Muneya Matsui: Graduate School of Economics, University of Tokyo
Akimichi Takemura: Graduate School of Information Science and Technology, University of Tokyo

No CIRJE-F-384, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: We consider goodness-of fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponentƒ¿ estimated from the data. We treat ƒ¿ as an unknown parameter, but for theoretical simplicity we also consider the case that ƒ¿ is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions.

Pages: 31 pages
Date: 2005-10
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2005cf384

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