Department of Economics and Business Economics

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

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A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. / Podolskij, Mark; Ziggel, Daniel.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2008.

Research output: Working paperResearch

Harvard

APA

CBE

Podolskij M, Ziggel D. 2008. A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Podolskij, Mark and Daniel Ziggel A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. Aarhus: Institut for Økonomi, Aarhus Universitet. 2008., 23 p.

Vancouver

Podolskij M, Ziggel D. A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. Aarhus: Institut for Økonomi, Aarhus Universitet. 2008.

Author

Podolskij, Mark ; Ziggel, Daniel. / A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. Aarhus : Institut for Økonomi, Aarhus Universitet, 2008.

Bibtex

@techreport{568f3b8021a911ddbe51000ea68e967b,
title = "A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models",
abstract = "We propose a new test for the parametric form of the volatility function in continuoustime diffusion models of the type dXt = a(t;Xt)dt + (t;Xt)dWt. Our approach involvesa range-based estimation of the integrated volatility and the integrated quarticity, whichare used to construct the test statistic. Under rather weak assumptions on the drift andvolatility we prove weak convergence of the test statistic to a centered mixed Gaussiandistribution. 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 parametricbootstrap procedure which provides a better approximation of the distribution of the teststatistic. Finally, it is demonstrated by means of Monte Carlo study that the range-basedtest is more powerful than the return-based test when comparing at the same samplingfrequency.",
keywords = "Bipower Variation; Central Limit Theorem; Diffusion Models; Goodness-Of- Fit Testing; High-Frequency Data; Integrated Volatility; Range-Based Bipower Variation; Semimartingale Theory",
author = "Mark Podolskij and Daniel Ziggel",
year = "2008",
language = "English",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models

AU - Podolskij, Mark

AU - Ziggel, Daniel

PY - 2008

Y1 - 2008

N2 - We propose a new test for the parametric form of the volatility function in continuoustime diffusion models of the type dXt = a(t;Xt)dt + (t;Xt)dWt. Our approach involvesa range-based estimation of the integrated volatility and the integrated quarticity, whichare used to construct the test statistic. Under rather weak assumptions on the drift andvolatility we prove weak convergence of the test statistic to a centered mixed Gaussiandistribution. 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 parametricbootstrap procedure which provides a better approximation of the distribution of the teststatistic. Finally, it is demonstrated by means of Monte Carlo study that the range-basedtest is more powerful than the return-based test when comparing at the same samplingfrequency.

AB - We propose a new test for the parametric form of the volatility function in continuoustime diffusion models of the type dXt = a(t;Xt)dt + (t;Xt)dWt. Our approach involvesa range-based estimation of the integrated volatility and the integrated quarticity, whichare used to construct the test statistic. Under rather weak assumptions on the drift andvolatility we prove weak convergence of the test statistic to a centered mixed Gaussiandistribution. 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 parametricbootstrap procedure which provides a better approximation of the distribution of the teststatistic. Finally, it is demonstrated by means of Monte Carlo study that the range-basedtest is more powerful than the return-based test when comparing at the same samplingfrequency.

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

M3 - Working paper

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

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -