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

Publikation: Working paperForskning

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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, 2007.

Publikation: Working paperForskning

Harvard

APA

CBE

Podolskij M, Ziggel D. 2007. A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Podolskij, Mark og Daniel Ziggel A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models. Aarhus: Institut for Økonomi, Aarhus Universitet. 2007., 23 s.

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. 2007.

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, 2007.

Bibtex

@techreport{01f895d0dece11dc9f8a000ea68e967b,
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 + s(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.Moreover, we present a parametric bootstrap procedure which provides a betterapproximation of the distribution of the test statistic. Finally, it is demonstrated by meansof Monte Carlo study that the range-based test is more powerful than the return-based testwhen 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",
author = "Mark Podolskij and Daniel Ziggel",
year = "2007",
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 - 2007

Y1 - 2007

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 + s(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.Moreover, we present a parametric bootstrap procedure which provides a betterapproximation of the distribution of the test statistic. Finally, it is demonstrated by meansof Monte Carlo study that the range-based test is more powerful than the return-based testwhen comparing at the same sampling frequency.

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 + s(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.Moreover, we present a parametric bootstrap procedure which provides a betterapproximation of the distribution of the test statistic. Finally, it is demonstrated by meansof Monte Carlo study that the range-based test is more powerful than the return-based testwhen comparing at the same sampling frequency.

KW - Bipower Variation; Central Limit Theorem; Diffusion Models; Goodness-Of-

KW - Fit Testing; High-Frequency Data; Integrated Volatility; Range-Based Bipower Variation;

KW - 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 -