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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Abstract

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

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

Dates
First available in Project Euclid: 5 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1383661268

Digital Object Identifier
doi:10.1214/13-AOS1153

Mathematical Reviews number (MathSciNet)
MR3127870

Zentralblatt MATH identifier
1292.62126

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1383661268


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References

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