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

Tobias Fissler () and Mark Podolskij ()
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Tobias Fissler: University of Bern, Postal: Department of Mathematics and Statistics, Institute of Mathematical Statistics, and Actuarial Science, Sidlerstrasse 5, 3012 Bern, Switzerland
Mark Podolskij: Aarhus University and CREATES, Postal: Department of Mathematics, University of Aarhus, Ny Munkegade 118, 8000 Aarhus C, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: continuous Itô semimartingales; high frequency data; microstructure noise; rank testing; stable convergence (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
Pages: 39
Date: 2014-12-10
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-mst and nep-ore
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