A restricted B-spline estimation of diffusion processes with applications to financial data

doi:10.7523/j.issn.2095-6134.2018.01.002

›› 2018, Vol. 35 ›› Issue (1): 10-17.DOI: 10.7523/j.issn.2095-6134.2018.01.002

Previous Articles Next Articles

A restricted B-spline estimation of diffusion processes with applications to financial data

HOU Yangyang, XU Tiange

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-12-27 Revised:2017-03-01 Online:2018-01-15
Supported by:
Supported by the National Nature Science Foundation of China (11101419)

Abstract

Abstract: Time-homogeneous diffusion process plays an important role in the financial market, and it is widely used for describing the stochastic dynamics of the underlying economic variables. In this work, we study nonparametric estimation of the drift and diffusion functions for the time-homogeneous diffusion process, and propose a new nonparametric regression technique based on higher-order approximations, which is called B-spline approach. The nonnegativity of the diffusion function is guaranteed by the restricted B-spline method. Our simulation results show that our method indeed outperforms the local polynomial method.

Key words: B-spline, time-homogeneous diffusion process, volatility

CLC Number:

TB114

HOU Yangyang, XU Tiange. A restricted B-spline estimation of diffusion processes with applications to financial data[J]. , 2018, 35(1): 10-17.

References

[1] Hansen L P, Scheinkman J A. Back to the future:generating moment implications for continuous-time Markov processes[J]. Econometrica, 1995, 63(4):767-804.
[2] Pedersen A R. Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes[J]. Bernoulli, 1995, 1(3):257-279.
[3] Aït-Sahalia, Yacine. Maximum likelihood estimation of discretely sampled diffusions:a closed-form approximation approach[J]. Econometrica, 2002, 70(1):223-262.
[4] Florens-Zmirou D. On estimating the diffusion coefficient from discrete observations[J]. Journal of Applied Probability, 1993, 30(4):790-804.
[5] Jiang G J, Knight J L. A nonparametric approach to the estimation of diffusion processes:with an application to a short-term interest rate model[J]. Econometric Theory, 1997, 13(5):615-645.
[6] Stanton R. A nonparametric model of term structure dynamics and the market price of interest rate risk[J]. The Journal of Finance, 1997, 52(5):1973-2002.
[7] Fan J, Zhang C. A reexamination of diffusion estimators with applications to financial model validation[J]. Journal of the American Statistical Association, 2003, 98(461):118-134.
[8] Ziegelmann F A. Nonparametric estimation of volatility functions:the local exponential estimator[J]. Econometric Theory, 2002, 18(4):985-991.
[9] Yu K, Jones M C. Likelihood-based local linear estimation of the conditional variance function[J]. Journal of the American Statistical Association, 2004, 99(465):139-144.
[10] Xu K L. Reweighted functional estimation of diffusion models[J]. Econometric Theory, 2010, 26(2):541-563.
[11] Yu Y, Yu K, Wang H, et al. Semiparametric estimation for a class of time-inhomogeneous diffusion processes[J]. Statistica Sinica, 2009, 19(2):843-867.
[12] Ramsay J O, Silverman B W. Functional data analysis[M]. New York:Springer, 2005.
[13] Ruppert D. Selecting the number of knots for penalized splines[J]. Journal of computational and graphical statistics, 2002, 11(4):735-757.
[14] Yoshimoto F, Harada T, Yoshimoto Y. Data fitting with a spline using a real-coded genetic algorithm[J]. Computer-Aided Design, 2003, 35(8):751-760.
[15] Fan J, Fan Y, Jiang J. Dynamic integration of time-and state-domain methods for volatility estimation[J]. Journal of the American Statistical Association, 2007, 102(478):618-631.
[16] Kloeden P E. On effects of discretization on estimators of drift parameters for diffusion processes[J]. Journal of Applied Probability, 1996, 33(4):606-610.
[17] Franke J, Kreiss J P, Mammen E. Bootstrap of kernel smoothing in nonlinear time series[C]//Bernoulli. Humboldt University of Berlin, Interdisciplinary Research Project 373:Quantification and Simulation of Economic Processes, 1997:1-37.

A restricted B-spline estimation of diffusion processes with applications to financial data

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics

Comments