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October 2013 A test for the rank of the volatility process: The random perturbation approach
Jean Jacod, Mark Podolskij
Ann. Statist. 41(5): 2391-2427 (October 2013). DOI: 10.1214/13-AOS1153


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.


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Jean Jacod. Mark Podolskij. "A test for the rank of the volatility process: The random perturbation approach." Ann. Statist. 41 (5) 2391 - 2427, October 2013.


Published: October 2013
First available in Project Euclid: 5 November 2013

zbMATH: 1292.62126
MathSciNet: MR3127870
Digital Object Identifier: 10.1214/13-AOS1153

Primary: 60F05 , 60F17 , 62E20 , 62M07

Keywords: central limit theorem , High frequency data , homoscedasticity testing , Itô semimartingales , rank estimation , stable convergence

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 5 • October 2013
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