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Testing the parametric form of the volatility in continuous time diffusion models: an empirical process approach

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  • Dette, Holger
  • Podolskij, Mark

Abstract

In this paper we present two new tests for the parametric form of the variance function in difusion processes dXt = b(t;Xt)+ó(t;Xt)dWt: Our approach is based on two stochastic processes of the integrated volatility. We prove weak convergence of these processes to centered processes whose conditional distributions given the process (Xt)t2[0;1] are Gaussian. In the special case of testing for a constant volatility the limiting process is the standard Brownian bridge in both cases. As a consequence an asymptotic distribution free test (for the problem of testing for homoscedasticity) and bootstrap tests (for the problem of testing for a general parametric form) can easily be implemented. It is demonstrated that the new tests are more powerful with respect to Pitman alternatives than the currently available procedures for this problem. The asymptotic advantages of the new approach are also observed for realistic sample sizes in a simulation study, where the finite sample properties of a Kolmogorov-Smirnov test are investigated.

Suggested Citation

  • Dette, Holger & Podolskij, Mark, 2005. "Testing the parametric form of the volatility in continuous time diffusion models: an empirical process approach," Technical Reports 2005,50, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200550
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    References listed on IDEAS

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    Cited by:

    1. Mark Podolskij & Daniel Ziggel, 2007. "A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models," CREATES Research Papers 2007-26, Department of Economics and Business Economics, Aarhus University.
    2. Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.
    3. Dette, Holger & Podolskij, Mark, 2008. "Testing the parametric form of the volatility in continuous time diffusion models--a stochastic process approach," Journal of Econometrics, Elsevier, vol. 143(1), pages 56-73, March.

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