A test for the rank of the volatility process: the random perturbation approach
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.
References listed on IDEAS
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- Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
- Robin, Jean-Marc & Smith, Richard J., 2000.
"Tests Of Rank,"
Cambridge University Press, vol. 16(02), pages 151-175, April.
- Robin, J.M. & Smith, R.J., 1995. "Tests of Rank," Cambridge Working Papers in Economics 9521, Faculty of Economics, University of Cambridge.
- Jean-Marc Robin & Richard J. Smith, 2000. "Tests of rank," Post-Print hal-00357758, HAL.
- Mark Podolskij & Mathieu Rosenbaum, 2012. "Testing the local volatility assumption: a statistical approach," Annals of Finance, Springer, vol. 8(1), pages 31-48, February.
- Mark Podolskij & Mathieu Rosenbaum, 2011. "Testing the local volatility assumption: a statistical approach," CREATES Research Papers 2011-04, Department of Economics and Business Economics, Aarhus University.
- Susanne Ditlevsen & Michael Sørensen, 2004. "Inference for Observations of Integrated Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 417-429. Full references (including those not matched with items on IDEAS)
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