IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v4y1988i03p384-402_01.html
   My bibliography  Save this article

Some Exact Formulae for Autoregressive Moving Average Processes

Author

Listed:
  • Zinde-Walsh, Victoria

Abstract

This paper demonstrates that for a finite stationary autoregressive moving average process the inverse of the covariance matrix differs from the matrix of the covariances of the inverse process by a matrix of low rank. The formula for the exact inverse of the covariance matrix of the scalar or multivariate process is provided. We obtain approximations based on this formula and evaluate some of the approximate results in the existing literature. Applications to computational algorithms and to the distributions of two-step estimators are discussed. In addition the paper contains the formula for the determinant of the covariance matrix which is useful in exact maximum likelihood estimation; it also lists the expressions for the autocovariances of scalar autoregressive moving average processes.

Suggested Citation

  • Zinde-Walsh, Victoria, 1988. "Some Exact Formulae for Autoregressive Moving Average Processes," Econometric Theory, Cambridge University Press, vol. 4(3), pages 384-402, December.
    • Handle: RePEc:cup:etheor:v:4:y:1988:i:03:p:384-402_01
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466600013360/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. David F. Findley & Demetra P. Lytras & Agustin Maravall, 2016. "Illuminating ARIMA model-based seasonal adjustment with three fundamental seasonal models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 11-52, March.
    2. Paulina Granados Z., 2004. "Income Function of Chilean Households: Life Cicle and Persistence of Shocks," Working Papers Central Bank of Chile 257, Central Bank of Chile.
    3. McLeod, A.I. & Zhang, Y., 2008. "Faster ARMA maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2166-2176, January.
    4. Choudhury, Askar H. & Power, Simon, 1995. "A new approximate GLS estimator for the linear regression model with ARMA(p, q) disturbances," Economics Letters, Elsevier, vol. 48(2), pages 119-127, May.
    5. McLeod, A. Ian & Yu, Hao & Krougly, Zinovi L., 2007. "Algorithms for Linear Time Series Analysis: With R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i05).
    6. Peter C.B. Phillips, 1990. "Operational Algebra and Regression t-Tests," Cowles Foundation Discussion Papers 948, Cowles Foundation for Research in Economics, Yale University.
    7. Galbraith, JohnW. & Zinde-Walsh, Victoria, 1999. "On the distributions of Augmented Dickey-Fuller statistics in processes with moving average components," Journal of Econometrics, Elsevier, vol. 93(1), pages 25-47, November.
    8. Wilfredo Palma & Mauricio Zevallos, 2004. "Analysis of the correlation structure of square time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 529-550, July.
    9. Paulina Granados Z., 2004. "Chilean Household Income Function: Life Cycle and Persistence of Shocks," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 7(1), pages 51-89, April.
    10. vdr Leeuw, J.L., 1997. "Maximum Likelihood Estimation of Exact ARMA Models," Other publications TiSEM a1cdd9b8-93d9-460c-a0c9-1, Tilburg University, School of Economics and Management.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:4:y:1988:i:03:p:384-402_01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.