Computational Economics 17: 179–201, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 179 Robust Estimation of GARMA Model Parameters with an Application to Cointegration among Interest Rates of Industrialized Countries RAJALAKSHMI RAMACHANDRAN and PAUL BEAUMONT Department of Economics, Florida State University, Tallahassee, FL 32303, U.S.A.; E-mail: ramachan@csee.usf.edu and beaumont@scri.fsu.edu Abstract. We review the literature on long memory ARFIMA and GARMA models and introduce a new efficient estimator for GARMA models, which we show to be robust. Next we conduct a Monte Carlo study to demonstate the power of the Dickie–Fuller test when the data are generated from a stationary GARMA process. We conclude with a brief discussion of cointegration in the context of GARMA models with an application to international interest rates. Key words: long memory processes, GARMA models, fractional integration, Dickey–Fuller tests, comovement, cointegration, international interest rates 1. Introduction Most economic and financial variables exhibit temporal correlation. The dynamics of these variables may be studied in either the time domain using Autoregress- ive Moving Average (ARMA) models or in the frequency domain using spectral analysis. ARMA models assume that the data process is stationary and that the autocorrelation function decays exponentially so that there is no strong dependence between distant observations. The Fourier transform of such an autocorrelation function produces a spectrum that is finite at all frequencies. Autoregressive Integ- rated Moving Average (ARIMA) models generalize ARMA models by allowing the d th difference (where d is a positive integer) of a process to be ARMA. An AR- IMA process exhibits a special type of nonstationarity in which the autocorrelation function does not decay at all and the spectrum is unbounded at the origin (zero frequency). Autoregressive Fractionally Integrated Moving Average (ARFIMA) models are more general still, allowing the difference parameter d to be fractional. The autocorrelation function of an ARFIMA process dies off hyperbolically (more slowly than exponential) and so allows for long-term dependency or long memory in the process. For some values of d the spectrum is bounded at all frequencies and for others the spectrum is unbounded at the origin. A model encompassing all these as special cases is the Generalized Autoregressive Moving Average (GARMA)