72
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Non parametric estimation of transition density for second-order diffusion processes

, &
Pages 5840-5852 | Received 28 Nov 2022, Accepted 04 Jul 2023, Published online: 21 Jul 2023

References

  • AlÏt-Sahalia, Y. 1999. Transition densities for interest rate and other nonlinear diffusions. The Journal of Finance 54 (4):1361–95.
  • AlÏt-Sahalia, Y. 2002. Maximum likelihood estimation of discretely sampled diffusions: A closed form approximation approach. Econometrica 70 (1):223–62.
  • Bandi, F. M., and T. H. Nguyen. 2003. On the functional estimation of jump–diffusion models. Journal of Econometrics 116 (1-2):293–328. doi: 10.1016/S0304-4076(03)00110-6.
  • Botev, Z. I., J. F. Grotowski, and D. P. Kroese. 2010. Kernel density estimation via diffusion. The Annals of Statistics 38 (5):2916–57. doi: 10.1214/10-AOS799.
  • Brandt, M. W, and P. Santa-Clara. 2002. Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. Journal of Financial Economics 63 (2):161–210. doi: 10.1016/S0304-405X(01)00093-9.
  • Chen, S. X., J. T. Gao, and C. Y. Tang. 2008. A test for model specification of diffusion processes. The Annals of Statistics 36 (1):167–98. doi: 10.1214/009053607000000659.
  • Choi, S. 2015. Explicit form of approximate transition probability density functions of diffusion processes. Journal of Econometrics 187 (1):57–73. doi: 10.1016/j.jeconom.2015.02.003.
  • Christensen, B. J., R. Poulsen, and M. Sørensen. 2001. Optimal inference in diffusion models of the short rate of interest. Working Paper No. 102. Centre for Analytical Finance, University of Aarhus, Aarhus School of Business, Aarhus, Denmark.
  • Ditlevsen, S., and M. Sorensen. 2004. Inference for observations of integrated diffusion processes. Scandinavian Journal of Statistics 31 (3):417–29. doi: 10.1111/j.1467-9469.2004.02_023.x.
  • Florens-Zmirou, D. 1993. On estimating the diffusion coefficient from discrete observations. Journal of Applied Probability 30 (4):790–804. doi: 10.2307/3214513.
  • Hirukawa, M., and M. Sakudo. 2014. Nonnegative bias reduction methods for density estimation using asymmetric kernels. Computational Statistics & Data Analysis 75:112–23. doi: 10.1016/j.csda.2014.01.012.
  • Hyndman, R. J., D. M. Bashtannyk, and G. K. Grunwald. 1996. Estimating and visualizing conditional densities. Journal of Computational and Graphical Statistics 5 (4):315–36. doi: 10.1080/10618600.1996.10474715.
  • Hyndman, R. J., and Q. Yao. 2002. Nonparametric estimation and symmetry tests for conditional density functions. Journal of Nonparametric Statistics 14 (3):259–78. doi: 10.1080/10485250212374.
  • Igarashi, G., and Y. Kakizawa. 2020. Multiplicative bias correction for asymmetric kernel density estimators revisited. Computational Statistics & Data Analysis 141:40–61. doi: 10.1016/j.csda.2019.06.010.
  • Mombeni, H. A., B. Mansouri, and M. R. Akhoond. 2021. Asymmetric kernels for boundary modification in distribution function estimation. REVSTAT-Statistical Journal 19 (4):463–84.
  • Nadaraya, E. A. 1964. On estimating regression. Theory of Probability & Its Applications 9 (1):141–2. doi: 10.1137/1109020.
  • Nicolau, J. 2007. Nonparametric estimation of second-order stochastic differential equations. Econometric Theory 23 (05):880. doi: 10.1017/S0266466607070375.
  • Ouazza, A., N. Rhomari, and Z. Zarrouk. 2022. Kernel method to estimate nonlinear structural equation models. Quality & Quantity 56 (5):3465–80. doi: 10.1007/s11135-021-01274-9.
  • Rosenblatt, M. 1969. Conditional probability density and regression estimators. Multivariate Analysis II 25:31.
  • Song, Y. 2020. Nonparametric estimation for second-order jump-diffusion model in high frequency data. The Singapore Economic Review 65 (04):1033–63. doi: 10.1142/S0217590817500102.
  • Zhou, S. Y. 2012. Study on transition density of diffusion process. Master’s thesis. Nanjing University of Science and Technology, Nanjing.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.