The Annals of Statistics

A test for the rank of the volatility process: The random perturbation approach

Jean Jacod and Mark Podolskij

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In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Itô semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Itô semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.

Article information

Ann. Statist., Volume 41, Number 5 (2013), 2391-2427.

First available in Project Euclid: 5 November 2013

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Zentralblatt MATH identifier

Primary: 62M07: Non-Markovian processes: hypothesis testing 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory 60F17: Functional limit theorems; invariance principles

Central limit theorem high frequency data homoscedasticity testing Itô semimartingales rank estimation stable convergence


Jacod, Jean; Podolskij, Mark. A test for the rank of the volatility process: The random perturbation approach. Ann. Statist. 41 (2013), no. 5, 2391--2427. doi:10.1214/13-AOS1153.

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