Skip to main content
SpringerLink
Log in

Normalizing transformations of some statistics of Gaussian ARMA processes

  • Time Series Analysis
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In this paper, the authors investigate Edgeworth type expansions of certain transformations of some statistics of Gaussian ARMA processes. They also investigate transformations which will make the second order part of the Edgeworth expansions vanish. Some numerical studies are made and they show that the above transformations give better approximations than the usual approximation.

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

  • Fang, C. and Krishnaiah, P. R. (1982). Asymptotic joint distributions of the elements of sample covariance matrix, Statistics and Probability: Essays in Honor of C. R. Rao, 249–262, North-Holland, New York-Amsterdam.

    Google Scholar 

  • Fujikoshi, Y. and Ochi, Y. (1984). Asymptotic properties of the maximum likelihood estimate in the first order autoregressive process, Ann. Inst. Statist. Math., 36, 119–128.

    Google Scholar 

  • Konishi, S. (1978). An approximation to the distribution of the sample correlation coefficient, Biometrika, 65, 654–656.

    Google Scholar 

  • Konishi, S. (1981). Normalizing transformations of some statistics in multivariate analysis, Biometrika, 68, 647–651.

    Google Scholar 

  • Taniguchi, M. (1983). On the second order asymptotic efficiency of estimators of Gaussian ARMA processes, Ann. Statist, 11, 157–169.

    Google Scholar 

  • Taniguchi, M. (1986). Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes, J. Multivariate Anal., 18, 1–31.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Multivariate Analysis, University of Pittsburgh, Fifth Floor, Thackeray Hall, 15260, Pittsburgh, PA, U.S.A.

    M. Taniguchi, P. R. Krishnaiah & R. Chao

Authors
  1. M. Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. R. Krishnaiah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Chao
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work is supported by Contract N00014-K-0292 of the Office of Naval Research and Contract F49620-85-C-0008 of the Air Force Office of Scientific Research. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.

The work of this author was done at the Center for Multivariate Analysis. His permanent address is Department of Mathematics, Hiroshima University, Naka-ku, Hiroshima 730, Japan.

About this article

Cite this article

Taniguchi, M., Krishnaiah, P.R. & Chao, R. Normalizing transformations of some statistics of Gaussian ARMA processes. Ann Inst Stat Math 41, 187–197 (1989). https://doi.org/10.1007/BF00049117

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00049117

Key words and phrases

Search

Navigation