Metrika

, Volume 42, Issue 1, pp 331–339 | Cite as

A proof of asymptotic normality for some VARX models

  • Mohamed Boutahar
  • Claude Deniau
Article

Abstract

Here we present a proof of the asymptotic normality of least squares estimates for stable multivariate autoregressive models excited by a deterministic second order input signal.

Key Words

Conditional Lindeberg condition least squares estimates martingale difference persistent excitation stable autoregressive model spectral measure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bay EW, Sastry SS (1985) Persistency of excitation, sufficient richness and parameter convergence in discrete time adaptive control. System and control letters 6:153–163Google Scholar
  2. [2]
    Boutahar M (1991) Distribution asymptotique de l'estimateur des moindres carrés. Cas des modèlesARX(p, s) instables. Stochastics and Stochastics Report 37:105–126Google Scholar
  3. [3]
    Chan NH, Wei CZ (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. The Annals of Statistics 16, 1:367–401Google Scholar
  4. [4]
    Crowder M (1980) On the asymptotic properties of least squares in autoregression. The Annals of Statistics 8, 1:132–146Google Scholar
  5. [5]
    Dickey DA, Fuller WA (1979) Distribution of estimators for autoregressive times series with a unit root. J Amer Statist Ass 74:427–431Google Scholar
  6. [6]
    Lai TL, Wei CZ (1982) Least square estimates in stochastic regression models with application to identification and control of dynamic systems. The Annals of Statistics 10, 1:154–186Google Scholar
  7. [7]
    Lai TL, Wei CZ (1986) On the concept of excitaton in least square identification and adaptive control. Stochastics 16:227–254Google Scholar
  8. [8]
    Moore JB (1983) Persistence of excitation in extended least square. IEEE Trans Autom Control 28:60–68Google Scholar
  9. [9]
    Rauzy G (1976) Propriétés statistiques des suites arithmétiques. PUFGoogle Scholar
  10. [10]
    Reinsel G (1979) FIML estimation of the dynamic simultaneous equations models with ARMA disturbances. Journal of Econometrics 9, 3:263–291Google Scholar
  11. [11]
    Touati A (1990) Loi limite de l'estimateur des moindres carrés dans le modèle autorégressif mixte. Ann de L'IHP 26Google Scholar
  12. [12]
    Viano MC (1987) Degré d'excitation persistante et convergence presque sûre de l'estimateur des moindres carrés généralisé dans un modèle ARMAX. CRAS Tome 305, I, 6Google Scholar

Copyright information

© Physica-Verlag 1995

Authors and Affiliations

  • Mohamed Boutahar
    • 1
    • 2
  • Claude Deniau
    • 1
    • 2
  1. 1.Dépt. de MathématiquesFaculté des SciencesMarseille Cedex 9France
  2. 2.GREQAMMarseilleFrance

Personalised recommendations