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Re-weighted functional estimation of second-order diffusion processes

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Abstract

Second-order diffusion process can not only model integrated and differentiated diffusion processes but also overcome the difficulties associated with the nondifferentiability of the Brownian motion, so these models play an important role in econometric analysis. In this paper, we propose a re-weighted estimator of the diffusion coefficient in the second-order diffusion model. Consistence of the estimator is proved under appropriate conditions and the conditions that ensure the asymptotic normality are also stated. The performance of the proposed estimator is assessed by simulation study.

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References

  • Arnold L (1974) Stochastic differential equations: theory and application. Wiley, Amsterdam

    Google Scholar 

  • Bandi F, Phillips P (2003) Fully nonparametric estimation of scalar diffusion models. Econometrica 71: 241–283

    Article  MathSciNet  MATH  Google Scholar 

  • Bibby BM, Sørensen M (1995) Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1: 17–39

    Article  MathSciNet  MATH  Google Scholar 

  • Bibby BM, Jacobsen M, Sørensen M (2002) Estimating functions for discretely sampled diffusion-type models. In: Handbook of financial econometrics. North-Holland, Amsterdam

  • Cai Z (2001) Weighted Nadaraya-Watson regression estimation. Stat Probab Lett 51: 307–318

    Article  MATH  Google Scholar 

  • Cai Z (2002) Regression quantiles for time series. Econ Theory 18: 169–192

    Article  MATH  Google Scholar 

  • Comte F, Catalot VG, Rozenholc Y (2007) Penalized nonparametric mean square estimation of the coefficients of diffusion processes. Bernoulli 13: 514–543

    Article  MathSciNet  MATH  Google Scholar 

  • Dalalyan A (2005) Sharp adaptive estimation of the drift function for ergodic diffusions. Ann Stat 33: 2507–2528

    Article  MathSciNet  MATH  Google Scholar 

  • Ditlevsen PD, Ditlevsen S, Andersen KK (2002) The fast climate fluctuations during the stadial and interstadial climate states. Ann Glaciology 35: 457C462

    Google Scholar 

  • Ditlevsen S, Sørensen M (2004) Inference for observations of integrated diffusion processes. Scand J Stat 31: 417C429

    Article  Google Scholar 

  • Fan J, Gijbels I (1996) Local polynomial modeling and its applications. Chapman & Hall, London

    Google Scholar 

  • Fan J, Zhang C (2003) A re-examination of diffusion estimations with applications to financial model validation. J Am Stat Assoc 98: 118–134

    Article  MathSciNet  MATH  Google Scholar 

  • Gasser T, Muller HG (1979) Kernel estimation of regression function. In: Gasser T, Rosenblatt M (eds) Smoothing techniques for curve estimation. Springer, Heidelberg, pp 23–68

    Chapter  Google Scholar 

  • Gloter A (2000) Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient. Probab Stat 4: 204–227

    MathSciNet  Google Scholar 

  • Gloter A (2006) Parameter estimation for a discretely observed integrated diffusion process. Scand J Stat 33: 83–104

    Article  MathSciNet  MATH  Google Scholar 

  • Gobet E, Hoffmann M, Reiss M (2004) Nonparametric estimation of scalar diffusions based on low frequency data. Ann Stat 32: 2223–2253

    Article  MathSciNet  MATH  Google Scholar 

  • Hall P, Huang LS (2001) Nonparametric kernel regression subject to monotonicity constraints. Ann Stat 29: 624–647

    Article  MathSciNet  MATH  Google Scholar 

  • Hall P, Presnell B (1999) Intentionally biased bootstrap methods. J R Stat Soc B 61: 143–158

    Article  MathSciNet  MATH  Google Scholar 

  • Hall P, Wolff RCL, Yao Q (1999) Methods for estimating a conditional distribution function. J Am Stat Assoc 94: 154–163

    Article  MathSciNet  MATH  Google Scholar 

  • Karlin S, Taylor HM (1981) A second course in stochastic processes. Academic Press, New York

    MATH  Google Scholar 

  • Nicolau J (2007) Nonparametric estimation of scend-order stochastic differential equations. Econ Theory 23: 880–898

    Article  MathSciNet  MATH  Google Scholar 

  • Owen AB (2001) Empirical likelihood. Chapman & Hall, London

    Book  MATH  Google Scholar 

  • Rogers LCG, Williams D (2000) Diffusions, Markov processes, and Martingales, vol 2. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Spokoiny VG (2000) Adaptive drift estimation for nonparametric diffusion model. Ann Stat 28: 815–836

    Article  MathSciNet  MATH  Google Scholar 

  • Wang HC, Lin ZY (2010) Local liner estimation of second-order diffusion models. Commun Stat Theor M (in press)

  • Xu KL (2010) Re-weighted functional estimation of diffusion models. Econ Theory 26: 541–563

    Article  MATH  Google Scholar 

  • Xu KL, Phillips PCB (2011) Tilted nonparametric estimation of volatility functions with empirical applications. J Bus Econ Stat (in press)

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Yuquan Campus, No.38 Zheda Road, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Yunyan Wang

  2. Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People’s Republic of China

    Lixin Zhang

  3. School of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, People’s Republic of China

    Mingtian Tang

Authors
  1. Yunyan Wang
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  2. Lixin Zhang
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  3. Mingtian Tang
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Correspondence to Yunyan Wang.

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Wang, Y., Zhang, L. & Tang, M. Re-weighted functional estimation of second-order diffusion processes. Metrika 75, 1129–1151 (2012). https://doi.org/10.1007/s00184-011-0372-6

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  • DOI: https://doi.org/10.1007/s00184-011-0372-6

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