OJS  Vol.1 No.2 , July 2011
Some New Estimators of Integrated Volatility
Abstract: We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to moment problem. As the bandwidth of the kernel vanishes, an estimator of the instantaneous stochastic volatility is obtained. We also develop some new estimators based on smoothing splines.
Cite this paper: nullJ. Bishwal, "Some New Estimators of Integrated Volatility," Open Journal of Statistics, Vol. 1 No. 2, 2011, pp. 74-80. doi: 10.4236/ojs.2011.12008.

[1]   O. E. Barndorff-Nielsen and N. Shephard, “Non-gaussian Ornstein—Uhlenbeck-Based Models and Some of Their Uses in Financial Economics (with Discussion),” Journal of the Royal Statistical Society: Series B, Vol. 63, No. 2, 2001, pp. 167-241. doi:10.1111/1467-9868.00282

[2]   D. P. Foster and D. B. Nelson, “Continuous Record Asymptotics for Rolling Sampling Variance Estimators,” Econometrica, Vol. 64, No. 1, 1996, pp. 139-174. doi:10.2307/2171927

[3]   E. Andreou and E. Ghysels, “Rolling Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results,” Journal of Business and Economics Statistics, Vol. 20, No. 3, 2002, pp. 363-375. doi:10.1198/073500102288618504

[4]   O. E. Barndorff-Nielsen and N. Shephard, “Econometric Analysis of Realised Covariation: High Frequency Based Covariance, Regression and Correlation in Financial Economics,” Econometrica, Vol. 72, No. 3, 2004, pp. 885-925. doi:10.1111/j.1468-0262.2004.00515.x

[5]   O. E. Barndorff-Nielsen and N. Shephard, “Power and Bipower Variation with Stochastic Volatility and Jumps (with Discussion),” Journal of Financial Econometrics, Vol. 2, No. 1, 2004, pp. 1-48. doi:10.1093/jjfinec/nbh001

[6]   S. Zhang and R. J. Karunamuni: “On Kernel Density Estimation near Endpoints,” Journal of Statistical Planning and Inference, Vol. 70, No. 2, 1988, pp. 301-316. doi:10.1016/S0378-3758(97)00187-0

[7]   J. P. N. Bishwal, “Parameter Estimation in Stochastic Differential Equations,” Springer-Verlag, Berlin, 2008. doi:10.1007/978-3-540-74448-1

[8]   D. Kristensen, “Nonparametric Filtering of the Realised Volatilty: A Kernel Based Approach,” Econometric Theory, Vol. 26, No. 1, 2010, pp. 60-93. doi:10.1017/S0266466609090616

[9]   C. Gu, “Smoothing Spline ANOVA Models,” Springer- Verlag, New York, 2002.

[10]   P. Hall and J. S. Marron, “On Variance Estimation in Nonparametric Regression,” Biometrika, Vol. 77, No. 2, 1990, pp. 415-419. doi:10.1093/biomet/77.2.415

[11]   G. Wahba, “Spline Models for Observational Data,” CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, September 1990.