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A Journal of Theoretical and Applied Statistics
Volume 57, 2023 - Issue 3
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Research Article

Bias reduction estimation for drift coefficient in diffusion models with jumps

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Pages 597-616 | Received 21 Sep 2018, Accepted 06 Apr 2023, Published online: 17 Apr 2023

References

  • Arfi M. Nonparametric drift estimation from ergodic samples. J Nonparametr Statist. 1995;5:381–389.
  • Stanton R. A nonparametric model of term structure dynamics and the market price of interest rate risk. J Finance. 1997;52:1973–2002.
  • Jiang G, Knight J. A nonparametric approach to the estimation of diffusion processes with an application to a short-term interest rate model. Econ Theory. 1997;13:615–645.
  • Bandi F, Phillps P. Fully nonparametric estimation of scalar diffusion models. Econometrica. 2003;71:241–283.
  • Duffie D, Pan J, Singleton K. Transform analysis and asset pricing for affine jump-diffusions. Econometrica. 2000;68:1343–1376.
  • Johannes M. The economic and statistical role of jumps to interest rates. J Finance. 2004;59:227–260.
  • Aït-Sahalia Y, Jacod J. Testing for jumps in a discretely observed process. Ann Statist. 2009;37:184–222.
  • Cont R, Tankov P. Financial modelling with jump processes. Boca Raton: Chapman and Hall/CRC; 2004.
  • Das S. The surprise element: jumps in interest rates. J Econometrics. 2002;106:27–65.
  • Andersen T, Benzoni L, Lund J. Stochastic Volatility, Mean Drift, and Jumps in the Short-Term Interest Rate. Working paper: 2004. available on: https://www.researchgate.net/publication/228793214.
  • Bandi F, Nguyen T. On the functional estimation of jump-diffusion models. J Economet. 2003;116:293–328.
  • Hanif M. Local linear estimation of recurrent jump-diffusion models. Comm Statist Theory Methods. 2012;41:4142–4163.
  • Lin Z, Wang H. Empirical likelihood inference for diffusion processes with jumps. Sci China Math. 2010;53:1805–1816.
  • Hanif M, Wang H, Lin Z. Reweighted Nadaraya–Watson estimation of jump-diffusion models. Sci China Math. 2012;55:1005–1016.
  • Mies F. Estimation of state-dependent jump activity and drift for Markovian semimartingales. J Statist Plann Inference. 2020;210:114–140.
  • Park J, Wang B. Nonparametric estimation of jump diffusion models. J Economet. 2020;DOI:10.1016/j.jeconom.2020.07.020.
  • Liu N, Song K, Wang X. Convoluted smoothed kernel estimation for drift coefficients in jump-diffusion models. Comm Statist Theory Methods. 2021;DOI:10.1080/03610926.2021.1872641.
  • Mancini C. Non-parametric threshold estimation for models with stochastic diffusion coefficients and jumps. Scand J Statist. 2009;36:270–296.
  • Mancini C, Renò R. Threshold estimation of Markov models with jumps and interest rate modeling. J Economet. 2011;160:77–92.
  • Fan J, Gijbels I. Local polynomial modeling and its applications. New York: Chapman and Hall; 1996.
  • Fan J. Design-adaptive nonparametric regression. J Amer Statist Assoc. 1992;87:998–1004.
  • Jacod J, Shiryaev A. Limit theorems for stochastic processes. New York: Springer; 2003.
  • Meyn SR, Tweedie RL. Stability of Markovian processes II: continuous-time processes and sampled chains. Adv Appl Probab. 1993;25:487–517.
  • Menaldi JL, Robin M. Invariant measure for diffusions with jumps. Appl Math Optim. 1999;40:105–140.
  • Wee I. Recurrence and transience for jumpCdiffusion processes. Stoch Anal Appl. 2000;18:1055–1064.
  • Xu K, Phillips P. Tilted nonparametric estimation of volatility functions with empirical applications. J Bus Econ Stat. 2011;29:518–528.
  • Fan J, Zhang C. A reexamination of diffusion estimations with applications to financial model validation. J Amer Statist Assoc. 2003;98:118–134.
  • Fan J, Fan Y, Jiang J. Dynamic integration of time- and state-domain methods for volatility estimation. J Am Stat Assoc. 2007;102:618–631.
  • Aït-Sahalia Y, Fan J, Peng H. Nonparametric transition-based tests for jump diffusions. J Amer Statist Assoc. 2009;104:1102–1116.
  • Song Y, Wang H. Central limit theorems of local polynomial threshold estimators for diffusion processes with jumps. Scand J Statist. 2018;45:644–681.
  • Moloche G. Local nonparametric estimation of scalar diffusions. Working paper, MIT; 2001.
  • Mancini C. Estimation of the parameters of jump of a general Poisson-diffusion model. Scand Actuar J. 2004;2004:42–52.

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