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Estimation of a multivariate stochastic volatility density by kernel deconvolution

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  • Van Es, Bert
  • Spreij, Peter

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.

Suggested Citation

  • Van Es, Bert & Spreij, Peter, 2011. "Estimation of a multivariate stochastic volatility density by kernel deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 683-697, March.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:3:p:683-697
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. 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.
    3. Fabienne Comte, 2004. "Kernel deconvolution of stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 563-582, July.
    4. 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.
    5. 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.
    6. 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.
    7. Wand, M. P., 1998. "Finite sample performance of deconvolving density estimators," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 131-139, February.
    8. 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.
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    Cited by:

    1. Belomestny, Denis & Schoenmakers, John, 2015. "Statistical Skorohod embedding problem: Optimality and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 169-180.
    2. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.

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