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Estimation of a multivariate stochastic volatility density by kernel deconvolution

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  • Van Es, Bert
  • Spreij, Peter
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    Abstract

    We consider a continuous time stochastic volatility model. The model contains a stationary volatility process. We aim to estimate the multivariate density of the finite-dimensional distributions of this process. We assume that we observe the process at discrete equidistant instants of time. The distance between two consecutive sampling times is assumed to tend to zero. A multivariate Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the multivariate volatility density. An expansion of the bias and a bound on the variance are derived.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 3 (March)
    Pages: 683-697

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:683-697

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    Related research

    Keywords: Stochastic volatility models Multivariate density estimation Kernel estimator Deconvolution Mixing;

    References

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    1. F. Comte & V. Genon-Catalot & Y. Rozenholc, 2010. "Nonparametric estimation for a stochastic volatility model," Finance and Stochastics, Springer, vol. 14(1), pages 49-80, January.
    2. Wand, M. P., 1998. "Finite sample performance of deconvolving density estimators," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 131-139, February.
    3. Fabienne Comte, 2004. "Kernel deconvolution of stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 563-582, 07.
    4. F. Comte & V. Genon-Catalot, 2006. "Penalized Projection Estimator for Volatility Density," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(4), pages 875-893.
    5. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    6. Harry Zanten & Pawel Zareba, 2008. "A note on wavelet density deconvolution for weakly dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 207-219, June.
    7. Comte, F. & Dedecker, J. & Taupin, M.L., 2008. "Adaptive Density Estimation For General Arch Models," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1628-1662, December.
    8. Masry, Elias, 1993. "Strong consistency and rates for deconvolution of multivariate densities of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 53-74, August.
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