Skip to main content
SpringerLink
Log in

On selection of the order of the spectral density model for a stationary process

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

Summary

Let {X(t)} be a stationary process with mean zero and spectral densityg(x). We shall use akth order parametric spectral modelfτ(k)(x) for this process. Without Gaussianity we can obtain an estiamte of τ(k), say ĝt(k), by maximizing the quasi-Gaussian likelihood of this model. We can then construct the best linear predictor ofX(t), which is computed on the basis of the estimated spectral densityfĝt(k)(x). An asymptotic lower bound of the mean square error of the estimated predictor is obtained. The bound is attained ifk is selected by Akaike's information criterion.

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. Akaike, H. (1970). Statistical predictor identification,Ann. Inst. Statist. Math.,22, 203–217.

    Article  MathSciNet  Google Scholar 

  2. Akaike, H. (1974). A new look at the statistical model identification,IEEE Trans. Automat. Contr., AC-19, 716–723.

    Article  MathSciNet  Google Scholar 

  3. Brillinger, D. R. (1969). Asymptotic properties of spectral estimates of second order,Biometrika,56, 375–390.

    Article  MathSciNet  Google Scholar 

  4. Brillinger, D. R. (1975).Time Series: Data Analysis and Theory, Holt, Rinehart and Winston, New York.

    MATH  Google Scholar 

  5. Dunsmuir, W. and Hannan, E. J. (1976). Vector linear time series models,Adv. Appl. Prob.,8, 339–364.

    Article  MathSciNet  Google Scholar 

  6. Grenander, U. and Rosenblatt, M. (1957).Statistical Analysis of Stationary Time Series, Wiley, New York.

    MATH  Google Scholar 

  7. Hannan, E. J. (1970).Multiple Time Series, Wiley, New York.

    Book  Google Scholar 

  8. Shibata, R. (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process,Ann. Statist.,8, 147–164.

    Article  MathSciNet  Google Scholar 

  9. Taniguchi, M. (1979). On estimation of parameters of Gaussian stationary processes,J. Appl. Prob.,16, 575–591.

    Article  MathSciNet  Google Scholar 

  10. Walker, A. M. (1964). Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series,J. Aust. Math. Soc.,4, 363–384.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hiroshima University, Hiroshima, Japan

    Masanobu Taniguchi

Authors
  1. Masanobu Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Taniguchi, M. On selection of the order of the spectral density model for a stationary process. Ann Inst Stat Math 32, 401–419 (1980). https://doi.org/10.1007/BF02480345

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480345

Keywords

Search

Navigation