Department of Economics and Business Economics

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

Research output: Working paperResearch

  • School of Economics and Management
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages23
Publication statusPublished - 2008

    Research areas

  • Bipower Variation; Central Limit Theorem; Diffusion Models; Goodness-Of- Fit Testing; High-Frequency Data; Integrated Volatility; Range-Based Bipower Variation; Semimartingale Theory

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ID: 11320515