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Estimation of quadratic variation for two-parameter diffusions

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  • Réveillac, Anthony

Abstract

In this paper we give a central limit theorem for the weighted quadratic variation process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations of a two-parameter diffusion Y=(Y(s,t))(s,t)[set membership, variant][0,1]2 observed on a regular grid Gn form an asymptotically normal estimator of the quadratic variation of Y as n goes to infinity.

Suggested Citation

  • Réveillac, Anthony, 2009. "Estimation of quadratic variation for two-parameter diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1652-1672, May.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1652-1672
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    References listed on IDEAS

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    1. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(4), pages 677-719, August.
    2. Sanz, Marta, 1989. "r-variations for two-parameter continuous martingales and itô's formula," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 69-92, June.
    3. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    4. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
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    Cited by:

    1. Pakkanen, Mikko S., 2014. "Limit theorems for power variations of ambit fields driven by white noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1942-1973.

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