Estimation of a multivariate stochastic volatility density by kernel deconvolution
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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Volume (Year): 102 (2011)
Issue (Month): 3 (March)
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- 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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- 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.
- 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.
- 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.
- Wand, M. P., 1998. "Finite sample performance of deconvolving density estimators," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 131-139, February.
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