Skip to main content
SpringerLink
Log in

Semi-recursive nonparametric identification in the general sense of a nonlinear heteroscedastic autoregression

  • Estimation and Filtering
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We consider semi-recursive kernel estimates of conditional mean, volatility function, and sensitivity function for a nonlinear heteroscedastic autoregression. We find the principal parts of mean square errors for these estimates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Masry, E. and Tjøstheim, D., Nonparametric Estimation and Identification of Nonlinear ARCH Time Series, Econom. Theory, 1995, vol. 11, pp. 258–289.

    Article  Google Scholar 

  2. Härdle, W., Tsybakov, A., and Yang, L., Nonparametric Vector Autoregression, J. Statist. Planning Inference, 1998, vol. 68, pp. 221–245.

    Article  MATH  Google Scholar 

  3. Jang, L., Härdle, W., and Nielsen, J.P., Nonparametric Autoregression with Multiplicative Volatility and Additive Mean, J. Time Ser. Anal., 1999, vol. 20, no. 5, pp. 579–602.

    Article  MathSciNet  Google Scholar 

  4. Raibman, N.S., Chto takoe identifikatsiya (What is Identification), Moscow, Nauka, 1970.

    Google Scholar 

  5. Eykhof, P., System Identification and State Estimation, London: Wiley, 1974. Translated ubder the title Osnovy identifikatsii sistem upravleniya. Otsenivanie parametrov i sostoyaniya, Moscow, Mir, 1975.

    Google Scholar 

  6. Nadaraya, E.A., On Regression Estimates, Theor. Prob. App., 1964, vol. 19, no. 1, pp. 147–149.

    Google Scholar 

  7. Watson, G.S., Smooth Regression Analysis, Sankhya. Indian J. Statist., 1964, vol. A26, pp. 359–372.

    Google Scholar 

  8. Tjèstheim, D. and Auestad, B.H., Nonparametric Identification of Nonlinear Time Series: Projections, J. Am. Statist. Associat., 1994, vol. 89, no. 428. pp. 1398–1409.

    Article  Google Scholar 

  9. Walk, H., Strong Universal Pointwise Consistency of Recursive Kernel Regression Estimates, Ann. Inst. Statist. Math., 2001, vol. 53, no. 4, pp. 691–707.

    Article  MATH  MathSciNet  Google Scholar 

  10. Pashchenko, F.F., Sensitivity Function and Its Applications to Choosing the Optimal Model, in Sistemy upravleniya (Control Systems), Moscow: Nauka, 1973, pp. 72–78.

    Google Scholar 

  11. Koshkin, G.M., Deviation Moments of the Substitution Error and Its Piecewise Smooth Approximations, Sib. Mat. Zh., 1999, vol. 40, no. 3, pp. 605–618.

    MathSciNet  Google Scholar 

  12. Bosq, D. and Cheze-Payaud, N., Optimal Asymptotic Quadratic Error of Nonparametric Regression Function Estimates for a Continuous-Time Process from Sampled-Data, Statistics, 1999, vol. 32, pp. 229–247.

    Article  MATH  MathSciNet  Google Scholar 

  13. Kitaeva, A.V. and Koshkin, G.M., Recurrent Nonparametric Estimation of Functions from Functionals of Multidimensional Density and Their Derivatives, Autom. Remote Control, 2009, no. 3, pp. 389–407.

    Article  MathSciNet  Google Scholar 

  14. Kitaeva, A.V. and Koshkin, G.M., Neparametricheskoe otsenivanie funktsii ot uslovnykh momentov po mnogomernym nablyudeniyam s sils’nym peremeshivaniem (Nonparametric Estimation of Functions of Conditional Moments by Multidimensional Observations with Strong Mixing), Proc. 8th Int. Conf. “System Identification and Control Problems,” January 26–30, 2009, Moscow: Inst. Probl. Upravlen., 2009, pp. 1001–1018.

    Google Scholar 

  15. Billingsley, P., Convergence of Probability Measures, New York: Wiley, 1968. Translated under the title Skhodimosts’ veroyatnostnykh mer, Moscow: Nauka, 1977.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tomsk Polytechnical University, Tomsk, Russia

    A. V. Kitaeva

  2. Tomsk State University, Tomsk, Russia

    G. M. Koshkin

Authors
  1. A. V. Kitaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. M. Koshkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the Russian Foundation for Basic Research, project no. 09-08-00595-a.

Original Russian Text © A.V. Kitaeva, G.M. Koshkin, 2010, published in Avtomatika i Telemekhanika, 2010, No. 2, pp. 92–111.

This paper was recommended for publication by A.I. Kibzun, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kitaeva, A.V., Koshkin, G.M. Semi-recursive nonparametric identification in the general sense of a nonlinear heteroscedastic autoregression. Autom Remote Control 71, 257–274 (2010). https://doi.org/10.1134/S0005117910020086

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117910020086

Keywords

Search

Navigation