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.
"A test for the rank of the volatility process: The random perturbation approach." Ann. Statist. 41 (5) 2391 - 2427, October 2013. https://doi.org/10.1214/13-AOS1153