Testing the maximal rank of the volatility process for continuous diffusions observed with noise

Fissler, Tobias; Podolskij, Mark (2017). Testing the maximal rank of the volatility process for continuous diffusions observed with noise. Bernoulli, 23(4B), pp. 3021-3066. International Statistical Institute 10.3150/16-BEJ836

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In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high frequency observations, we construct a test statistic for the maximal rank of the time varying stochastic volatility process. Our methodology is based upon a combination of a matrix perturbation approach and pre-averaging. We will show the asymptotic mixed normality of the test statistic and obtain a consistent testing procedure. We complement the paper with a simulation and an empirical study showing the performances on finite samples.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Fissler, Tobias

Subjects:

500 Science > 510 Mathematics

ISSN:

1350-7265

Publisher:

International Statistical Institute

Funders:

[4] Swiss National Science Foundation
[UNSPECIFIED] “Ambit fields: Probabilistic properties and statistical inference” funded by Villum Fonden

Language:

English

Submitter:

Tobias Fissler

Date Deposited:

25 Jul 2017 09:50

Last Modified:

25 Jul 2017 09:50

Publisher DOI:

10.3150/16-BEJ836

Uncontrolled Keywords:

continuous Itô semimartingales; high frequency data; microstructure noise; rank testing; stable convergence

BORIS DOI:

10.7892/boris.100924

URI:

https://boris.unibe.ch/id/eprint/100924

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