高频数据瞬时波动率核估计的窗宽选择及算法研究

doi:10.16381/j.cnki.issn1003-207x.2018.07.001

Abstract

Abstract: The non-parametric estimator of spot volatility is the current focus due to its high accuracy. However, this estimator has to choose the optimal bandwidth in its application. There is difficulty in calculating the optimal bandwidth since some awkward unknown parameters emerge. In this paper, taking kernel estimator as the representative of non-parametric estimator for spot volatility, a data-driven algorithm of bandwidth selection has been constructed by adopting some idea of non-parametric regression. The stability of algorithm for selecting bandwidth is proved in the theory. It is shown that the algorithm is adaptive and convergent with a fast rate from the numerical examples and the convergence is independent on the original value. The proposed algorithm is conductive to the subsequent analysis of spot volatility.

Key words: spot volatility, bandwidth selection, kernel estimator

CLC Number:

O212

WANG Jiang-tao, ZHOU Yong. Bandwidth Selection for Kernel Estimator of Spot Volatility in High Frequency data and Algorithm Design[J]. Chinese Journal of Management Science, 2018, 26(7): 1-8.

References

[1] Engle R F, Rusell J R, Autoregressive conditional duration:A new model for irregular spaced transaction date[J]. Econometrics, 1982,36(1):1127-1162.

[2] Bollerslev T, Generalized autoregressive conditional heteroscedasticity[J]. Econometrics, 1986, 31(5):307-327.

[3] Vetter M. Estimation of integrated volatility of volatility with applications to goodness-of-fit testing[J]. Bernoulli,2015,21(4):2393-2418.

[4] Zhang Lan, Mykland P A, Ait-Sahalia Y. A tale of two time scale:determining integrated volatility with noisy high-frequency data[J]. Journal of The American Statistical Association, 2005,100(472):1394-1411.

[5] Jacod J, Li Yingying, Mykland P A,et al. Microstructure noise in the continuous case:the pre-averaging approach[J]. Stochastic Processes and their Applications, 2009,119(7):2249-2276.

[6] Barndorff-Nielsen O E, Hansen P R, Lunde A, et al. Multivariate realized kernels:Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading[J]. Journal of Econometrics, 2011,162(2):149-169.

[7] Fan Jianqing, Wang Yazhen. Spot volatility estimation for high-frequency data[J]. Statistics and Its Interface, 2008, 1(2):279-288.

[8] Kristensen D. Nonparametric filtering of the realized spot volatility:A Kernel-based approach[J]. Econometric Theory, 2010, 26(1):60-93.

[9] Zu Yang, Boswijk H P. Estimating spot volatility with high-frequency financial data[J]. Journal of Econometrics, 2014, 181(2):117-135.

[10] Sabel T, Schmidt-Hieber J, Munk A. Spot volatility estimation for high-frequency data:Adaptive estimation in practice[M]//Antoniadis A, Poggi T M, Brossat X. Modelling and stochastic learning for forecasting in high dimensions. New York:Springer, 2015:213-241.

[11] Mancini1 C, Mattiussi V, Renò R. Spot volatility estimation using delta sequences[J]. Finance Stochastic, 2015, 19:261-293.

[12] 沈根祥.基于门限双幂变差的资产价格时点波动非参数估计[J].中国管理科学,2016, 24(1):21-29.

[13] 吴鑫育,李心丹,马超群. 门限已实现随机波动率模型及其实证研究[J].中国管理科学,2017, 25(3):10-19.

[14] Figueroa-Lopez J E, Li C. Optimal Kernel estimation of spot volatility of stochastic differential equations[R]. Working Paper, Washington University, 2016.

[15] Protter P, Stochastic integration and differential equation[M]. 2nd Edition. New York:Springer -Verlag, 2004.

[16] Barndorff-Neilsen O E, Graversen S E, Jacod J, et al. Limit theorems for bipower variation in financial econometrics[J]. Econometric Theory, 2006,22(4):677-719.

[17] Blanke D, Estimating of local smoothness coefficients for continuous time processes[J]. Statistical Inference for Stochastic Processes, 2002, 5(1):65-93.

[18] Gasser T, Kneip A, Kohler W. A flexible and fast method for automatic smoothing[J]. Journal of the American Statistical Association,1991, 415(86):643-652.

Bandwidth Selection for Kernel Estimator of Spot Volatility in High Frequency data and Algorithm Design

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