基于近邻截断的跳跃扩散过程波动函数的设定检验

doi:10.16381/j.cnki.issn1003-207x.2020.07.005

Abstract

Abstract: Since the volatility function testing is sensitive to jumps in high frequency data, based on nearest neighbor truncation approach,new tests for volatility function form of jump diffusion models are constructed by thepartial sum residual processes. The tests approximating asymptotic properties and their bootstrap methods are investigated. The test statistics are asymptotically robust to the drift and jump terms in jump diffusions. Monte Carlo simulations show that the tests are robust to jumps, and have reasonable size and power performances. The proposed tests are applied to the data of Shanghai Interbank Offered Rate (Shibor), it is found that the jump robust tests can distinguish models better than non-robust tests.

Key words: volatility function, jump diffusion processes, specification test, partial sum processes, nearest neighbor truncation

CLC Number:

O212

CHEN Qiang, GONG Yu-ting. Specification Test of Volatility Functions in Jump Diffusion Processes using Nearest Neighbor Truncation[J]. Chinese Journal of Management Science, 2020, 28(7): 45-56.

References

[1] Aït-Sahalia Y. Testing continuous-time models of the spot interest rate[J]. Review of Financial Studies,1996,9(2):385-426.
[2] Chen Qiang,Zheng Xu,Pan Zhiyuan. Asymptotically distribution-free tests for the volatility function of a diffusion[J]. Journal of Econometrics,2015,184(1):124-144.
[3] Corradi V,White H. Specification tests for the variance of a diffusion[J]. Journal of Time Series Analysis,2002,20(3):253-270.
[4] Dette H,von Lieres und Wilkau C. On a test for a parametric form of volatility in continuous time financial models[J]. Finance and Stochastics,2003,7(3):363-384.
[5] Li F. Testing the parametric specification of the diffusion function in a diffusion process. Econometric Theory,2007,23(2):221-250.
[6] Dette H,Podolskij M. Testing the parametric form of the volatility in continuous time diffusion models-a stochastic process approach[J]. Journal of Econometrics,2008,143(1):56-73.
[7] 陈强,郑旭,许秀. 基于鞅转化的利率模型漂移函数的设定检验[J]. 管理科学学报,2014,17(11):43-56.
[8] Barndorff-Nielsen O E,Shephard N. Variation,jumps,market frictions and high frequency data in financial econometrics[C]. Advances in Economics and Econometrics. Theory and Applications,Ninth World Congress,2007,3:328-372.
[9] Aït-Sahalia Y. Disentangling diffusion from jumps[J]. Journal of Financial Economics,2004,74(3):487-528.
[10] Shimizu Y,Yoshida N. Estimation of parameters for diffusion processes with jumps from discrete observations[J]. Statistical inference for Stochastic Processes,2006,9(3):227-277.
[11] Andersen T G,Dobrev D,Schaumburg E. Jump-robust volatility estimation using nearest neighbor truncation[J]. Journal of Econometrics,2012,169(1):75-93.
[12] Andersen T G,Dobrev D,Schaumburg E. A robust neighborhood truncation approach to estimation of integrated quarticity[J].Econometric Theory,2014,30(1):3-59.
[13] Kwon Y,Lee C. Strong Feller property and irreducibility of diffusions with jumps[J]. Stochastics and Stochastic Reports,1999,67(1-2):147-157.
[14] Bandi F,Nguyen T.On the functional estimation of jump-diffusion models[J].Journal of Econometrics,2003,116(1):293-328.
[15] Mancini C. Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps[J]. Scandinavian Journal of Statistics,2009,36(2):270-296.
[16] Vetter M,Dette H. Model checks for the volatility under microstructure noise[J]. Bernoulli,2012,18(4):1421-1447.
[17] Khmaladze E.Martingale approach to the goodness of fit tests[J]. Theory of Probability and Its Application,1981,26(2):240-267.
[18] Monsalve-Cobis A,González-Manteiga W,Febrero-Bande Manuel,M. Goodness-of-fit test for interest rate models:an approach based on empirical processes[J]. Computational Statistics & Data Analysis,2011,55(12):3073-3092.
[19] Fan J,Zhang A. reexamination of diffusion estimators with applications to financial model validation[J]. Journal of the American Statistical Association,2003,98(461):118-134.
[20] Vasicek O. An equilibrium characterization of the term structure[J].Journal of Financial Economics,1977,5(2):177-188.
[21] Cox J,Ingersoll Jr J,Ross S. A theory of the term structure of interest rates[J]. Econometrica,1985,53(2):385-407.
[22] Chan K,Karolyi G,Longstaff F,et al. An empirical comparison of alternative models of the short-term interest rate[J].Journal of Finance,1992,47(3):1209-1227.
[23] Ahn D H,Gao B. A parametric nonlinear model of term structure dynamics[J]. Review of financial studies,1999,12(4):721-762.
[24] Lin B H,Yeh S K. Junp-diffusion interest rate process:an empirical examination[J]. Journal of Business Finance & Accounting,1999,26(7-8):967-995.
[25] Lee S,Mykland P. Jumps in financial markets:A new nonparametric test and jump dynamics[J]. Review of Financial Studies,2008,21(6):2535-2563.
[26] 洪永淼,林海.中国市场利率动态研究——基于短期国债回购利率的实证分析[J],经济学季刊,2006,5(2):511-532.
[27] 谈正达,胡海鸥. 短期利率跳跃-扩散模型的非参数门限估计[J]. 中国管理科学,2012,20(1):8-13.
[28] Kutoyants Y A. Efficiency of the empirical distribution for ergodic diffusion[J]. Bernoulli,1997,3(4):445-456.

Specification Test of Volatility Functions in Jump Diffusion Processes using Nearest Neighbor Truncation

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	LI Qing, ZHANG Hu. Single-index Nonparametric Option Pricing Model——A Modified Nonparametric Pricing Approach [J]. Chinese Journal of Management Science, 2020, 28(10): 43-53.
[2]	Yuan Hui-ling, XU Lu, Zhou Yong. Leverage Effect Combining Trading Information with Stochastic Microstructure Noise [J]. Chinese Journal of Management Science, 2020, 28(9): 12-22.
[3]	XU Bao-guang, LIU Qian-qian, GAO Min-gang. The Flight Delay Propagation Analysis based on Airport Busy State [J]. Chinese Journal of Management Science, 2019, 27(8): 87-95.
[4]	HE Di, ZHOU Yong. Modeling and Analyzing Liquidity in Stock Market Using Macroeconomic Factors Based on State Space Model [J]. Chinese Journal of Management Science, 2019, 27(5): 42-49.
[5]	JIANG Qing-shan, HUANG Can, LI Yi-jun. The Estimation, Classification and Monte Carlo Simulation for Semiparametric Spatial ZISF [J]. Chinese Journal of Management Science, 2019, 27(3): 20-29.
[6]	FU Qiang, ZHANG Xing-min. Optimal Rolling Window Selection for Time-Varying Parameter Model and Its Application [J]. Chinese Journal of Management Science, 2018, 26(8): 20-30.
[7]	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.
[8]	ZHANG Li, DENG Li-ying, ZHOU Yong. Contrarian Effect of Semi-Parametric Alpha Strategy [J]. Chinese Journal of Management Science, 2016, 24(12): 30-38.
[9]	LI Zhan-jiang, CHI Guo-tai, DANG Jun-zhang. The Evaluation Model of Business Project Overall Risks of Follower Banks Based on Copula [J]. Chinese Journal of Management Science, 2015, 23(1): 99-110.
[10]	HUANG Jin-bo, LI Zhong-fei, ZHOU Xian-bo. Sensitivity and Convexity of VaR (CVaR) and Their Kernel Estimator [J]. Chinese Journal of Management Science, 2014, 22(8): 1-9.
[11]	JIANG Chun-fu, YANG Yu-kuan. Tail Conditional Variance of Portfolio with Mixture of Elliptically Distributions [J]. Chinese Journal of Management Science, 2013, 21(4): 17-26.
[12]	JIANG Jia-dong, FENG Yun-cheng. Study on New Control Charts Based on the Latent Structure of Covariance Matrix [J]. Chinese Journal of Management Science, 2011, 19(3): 123-133.
[13]	CUI Jie, DANG Yao-guo, LIU Si-feng. An Improved Approach for Determining Weights of Attributes in Decision Making Based on Grey incidence [J]. Chinese Journal of Management Science, 2008, 16(5): 141-145.
[14]	MAO Ze-chun, LIU Jin-e. The Distribution about Numbers of Claims on Homogeneous Policyholders under NCD System and Stop Loss Insurance [J]. Chinese Journal of Management Science, 2005, (5): 1-5.
[15]	GAO Hong-zhong, REN Yan-yan . The Bivariate GPSJ Class and Its Application in Insurance [J]. Chinese Journal of Management Science, 2004, (5): 30-34.