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

Author

Listed:
  • Tobias Fissler

    (University of Bern)

  • Mark Podolskij

    (Aarhus University and CREATES)

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.

Suggested Citation

  • Tobias Fissler & Mark Podolskij, 2014. "Testing the maximal rank of the volatility process for continuous diffusions observed with noise," CREATES Research Papers 2014-52, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-52
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/14/rp14_52.pdf
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    References listed on IDEAS

    as
    1. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    2. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    3. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    continuous Itô semimartingales; high frequency data; microstructure noise; rank testing; stable convergence;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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