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

Abstract

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.

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Tobias Fissler. Mark Podolskij. "Testing the maximal rank of the volatility process for continuous diffusions observed with noise." Bernoulli 23 (4B) 3021 - 3066, November 2017. https://doi.org/10.3150/16-BEJ836

Information

Received: 1 October 2014; Revised: 1 January 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778278
MathSciNet: MR3654798
Digital Object Identifier: 10.3150/16-BEJ836

Keywords: continuous Itô semimartingales , High frequency data , microstructure noise , rank testing , stable convergence

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4B • November 2017
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