Skip to main content
Log in

Least squares estimator for regression models with some deterministic time varying parameters

  • Publications
  • Published:
Metrika Aims and scope Submit manuscript

Abstract

Here we study the least squares estimates in some regression models. We assume that the evolution of the parameter is linearly explosive (i.e. polynomial), or stable (i.e. sinusoidal). We prove the strong consistency, and establish the rate of convergence.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Boutahar M (1991) Asymptotic distribution of least squares estimates in unstable ARX(p, s) models. Stochastics and Stochastics Reports 37:105–126

    MathSciNet  Google Scholar 

  • Chen HF, Guo L (1991) Identification and stochastic adaptive control. Birkhäuser

  • Choi MD (1983) Tricks or treats with the hilbert matrix. Ann Math Month 90:301–312

    Article  MATH  Google Scholar 

  • Chow GC (1983) Econometrics. McGraw-Hill

  • Davidov G, Shavit A, Shinkin N, Koren Y (1992) Estimation of dynamical-varying parameters by internal model principle. IEEE Trans on Autom Contr 37(4):498–503

    Article  Google Scholar 

  • Duflo M (1990) Méthodes récursives aléatories. Masson

  • Lai TL, Wei CZ (1982) Least squares estimates in stochastic regression models with applications to identification and control of dynamics systems. The Annals of Statistics 10(1):154–166

    MathSciNet  Google Scholar 

  • Lai TL, Robbin H, Wei CZ (1978) Strong consistency of least squares estimates in Multiple Regression. Proc Nat Acad Sci USA, 3034–3036

  • Sant DT (1977) Generalized least squares applied to time varying parameter models. An of Econ and Soc Meas 6/3:301–310

    Google Scholar 

  • Stout WF (1974) Almost sure convergence. Academic Press

  • Tsypkin YZ, Bondarenko MV (1992) An optimal algorithm for identification of rapidly time varying systems. IEEE Trans on Autom Contr 37 n (2):237–239

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boutahar, M., Deniau, C. Least squares estimator for regression models with some deterministic time varying parameters. Metrika 43, 57–67 (1996). https://doi.org/10.1007/BF02613897

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02613897

Key Words

Navigation