Exact and asymptotic tests for possibly non-regular hypotheses on stochastic volatility models |
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Authors: | Jean-Marie Dufour,Pascale Val ry |
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Affiliation: | aMcGill University, Centre interuniversitaire de recherche en analyse des organisations (CIRANO), and Centre interuniversitaire de recherche en économie quantitative (CIREQ), Canada;bService de l’enseignement de la finance, École des Hautes Études Commerciales de Montréal (HEC-Montréal), 3000 chemin de la Côte-Sainte-Catherine Montréal, Québec, Canada H3T 2A7 |
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Abstract: | We study the problem of testing hypotheses on the parameters of one- and two-factor stochastic volatility models (SV), allowing for the possible presence of non-regularities such as singular moment conditions and unidentified parameters, which can lead to non-standard asymptotic distributions. We focus on the development of simulation-based exact procedures–whose level can be controlled in finite samples–as well as on large-sample procedures which remain valid under non-regular conditions. We consider Wald-type, score-type and likelihood-ratio-type tests based on a simple moment estimator, which can be easily simulated. We also propose a C(α)-type test which is very easy to implement and exhibits relatively good size and power properties. Besides usual linear restrictions on the SV model coefficients, the problems studied include testing homoskedasticity against a SV alternative (which involves singular moment conditions under the null hypothesis) and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors (which raises identification difficulties). Three ways of implementing the tests based on alternative statistics are compared: asymptotic critical values (when available), a local Monte Carlo (or parametric bootstrap) test procedure, and a maximized Monte Carlo (MMC) procedure. The size and power properties of the proposed tests are examined in a simulation experiment. The results indicate that the C(α)-based tests (built upon the simple moment estimator available in closed form) have good size and power properties for regular hypotheses, while Monte Carlo tests are much more reliable than those based on asymptotic critical values. Further, in cases where the parametric bootstrap appears to fail (for example, in the presence of identification problems), the MMC procedure easily controls the level of the tests. Moreover, MMC-based tests exhibit relatively good power performance despite the conservative feature of the procedure. Finally, we present an application to a time series of returns on the Standard and Poor’s Composite Price Index. |
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Keywords: | Testing Exact test Monte Carlo test Maximized Monte Carlo test Wald test LR test LM test mml86" > text-decoration:none color:black" href=" /science?_ob=MathURL&_method=retrieve&_udi=B6VC0-4VPV5MC-1&_mathId=mml86&_user=10&_cdi=5940&_rdoc=8&_acct=C000053510&_version=1&_userid=1524097&md5=ad7badcfac4a9cb1db745d29d391ed67" title=" Click to view the MathML source" alt=" Click to view the MathML source" >C(α ) test Homoskedasticity Stochastic volatility Two-factor volatility Identification Singular moment conditions Finance Stock prices |
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