• Bernoulli
  • Volume 23, Number 4B (2017), 3021-3066.

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

Tobias Fissler and Mark Podolskij

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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.

Article information

Bernoulli, Volume 23, Number 4B (2017), 3021-3066.

Received: October 2014
Revised: January 2016
First available in Project Euclid: 23 May 2017

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


Fissler, Tobias; Podolskij, Mark. Testing the maximal rank of the volatility process for continuous diffusions observed with noise. Bernoulli 23 (2017), no. 4B, 3021--3066. doi:10.3150/16-BEJ836.

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