IDEAS home Printed from
   My bibliography  Save this paper

Robust Estimation of GARMA Model Parameters and Application to Cointegration among Interest Rates of Industrialized Countries


  • Raji Ramachandran

    () (Florida State University)

  • Paul Beaumont

    () (Florida State University)


Theoretical predictions for and empirical analysis of real economic time series indicate that there is dependence among distant observations. Empirical autocorrelation functions of such data show high persistence, decay slowly and show persistent cyclical patterns. Long-memory models take these stylized facts into account. The two long-memory models currently in vogue are Autoregressive Fractionally Integrated Moving Average process (ARFIMA) and Generalized Autoregressive Moving Average processes (GARMA). ARFIMA models take into account persistence in auto-correlations, whereas GARMA models characterize both the persistence and the cyclical patterns in the auto-correlation function. In the estimation of GARMA model parameters, the periodicity parameter, eta, converges faster than the others. This makes gradient-based methods unsuitable for estimating all parameters simultaneously. Chung (1996) and Gray et. al (1989) use a grid search on eta while estimating the other parameters by gradient methods. Here, we evaluate bisection techniques for eta combined with the Davidon-Fletcher-Powell gradient method for the other parameters. Based on these studies, we propose a robust and fast algorithm for GARMA model parameter estimation, including the difficult to recover parameter ranges. Such parameter ranges are of interest to economic data. As an application of our estimation procedure, we perform cointegration analysis on the interest rates of the industrialized countries by modeling them as GARMA processes. We look for evidence of cointegration among long-term interest rates of these countries. This study is motivated by the observed persistent, somewhat sinusoidal (rather than monotonic) decline of the autocorrelation function of the error correction term. We find that interest rates are better modelled as GARMA rather than ARFIMA processes and certain systems of interest rates are cointegrated. Using GARMA produces estimates with lower standard errors than other long-memory models. Further, we find that the difference between mean-reverting and nonstationary processes need not be considered in establishing cointegration. Rapid establishment of stationarity is useful in cointegration studies. Hence, we examined the power of the Dickie-Fuller test using generated GARMA data. We find that this test fails to identify stationarity correctly.

Suggested Citation

  • Raji Ramachandran & Paul Beaumont, 1999. "Robust Estimation of GARMA Model Parameters and Application to Cointegration among Interest Rates of Industrialized Countries," Computing in Economics and Finance 1999 851, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:851

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item


    Access and download statistics


    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:sce:scecf9:851. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.