A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models

Mark Podolskij () and Daniel Ziggel ()
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Daniel Ziggel: School of Economics and Management, University of Aarhus, Denmark and CREATES, Postal: 8000 Aarhus C, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We propose a new test for the parametric form of the volatility function in continuous time diffusion models of the type dXt = a(t;Xt)dt + _(t;Xt)dWt. Our approach involves a range-based estimation of the integrated volatility and the integrated quarticity, which are used to construct the test statistic. Under rather weak assumptions on the drift and volatility we prove weak convergence of the test statistic to a centered mixed Gaussian distribution. As a consequence we obtain a test, which is consistent for any fixed alternative. We also provide a test for neighborhood hypotheses. Moreover, we present a parametric bootstrap procedure which provides a better approximation of the distribution of the test statistic. Finally, it is demonstrated by means of Monte Carlo study that the range-based test is more powerful than the return-based test when comparing at the same sampling frequency.

Keywords: Bipower Variation, Central Limit Theorem, Diffusion Models, Goodness-Of- Fit Testing, High-Frequency Data, Integrated Volatility, Range-Based Bipower Variation; Semimartingale Theory (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Pages: 23
Date: 2008-05-14
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mst
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Working Paper: A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2008-22

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