Abstract
We review the literature on long memory ARFIMA and GARMA models andintroduce a new efficient estimator for GARMA models, which we show to berobust. Next we conduct a Monte Carlo study to demonstate the power of theDickie–Fuller test when the data are generated from a stationary GARMAprocess. We conclude with a brief discussion of cointegration in the contextof GARMA models with an application to international interest rates.
Similar content being viewed by others
References
Baille, R.T. (1996). Long memory processes and fractional integration in econometrics. Journal of Econometrics, 73, 5–59.
Baille, R.T., Bollerslev, T. and Mikkelsen, H.-O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasitcity. Journal of Econometrics, 74, 3–30.
Barkoulas, J.T., Baum, C.F. and Oguz, G.S. (1996). Fractional dynamics in a system of long term international interest rates. Working Paper, Boston College.
Beveridge, G.S.G and Schechter, R.S. (1970). Optimization Theory and Practice.McGraw-Hill Book Company, ch. vii, pp. 189–193.
Cheung, Y.W. and Diebold, F.X. (1994). On maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean. Journal of Econometrics, 62, 301–316.
Chung, C.-F. (1996). On estimating a generalized long memory model. Journal of Econometrics, 73, 237–259.
Chung, C.-F. (1996). A generalized fractionally integrated autoregressive moving-average process. Journal of Time Series Analysis, 17(2), 111–140.
Cheung, Y.W. and Lai, K.S. (1993). A fractional cointegration analysis of purchasing power parity. Journal of Business and Economic Statistics, 11, 103–112.
Diebold, F.X. and Rudenbusch, G.D. (1991). On the power of Dickey-Fuller tests against fractional alternatives. Economics Letters, 35, 155–160.
Fox, R. and Taqqu, M.S. (1985). Noncentral limit theorems for quadratic forms in random variables having long-range dependence. Annals of Probability, 13, 428–446.
Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4, 221–238.
Granger C.W.J. (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics, 16, 121–130.
Gray, H.L., Zhang, N.-F. and Woodward, W.A. (1989). On generalized fractional processes. Journal of Time Series Analysis, 10(3), 233–257.
Hassler, U. and Wolters, J. (1994). On the power of unit root tests against fractional alternative. Economics Letters, 45, 1–5.
Hosking, J.R.M. (1981). Fractional differencing. Biometrika, 68, 165–176.
Hosking, J.R.M. (1984). Modeling persistence in hydrological time series using fractional differencing. Water Resources Research, 20(12), 1898–1908.
Lo, A.W. (1991). Long term memory in stock market pricess. Econometrica, 59, 1279–1313.
Lobato, I.N. and Savin, N.E. (1998). Real and spurious long-memory properties of stock market data. Journal of Business and Economic Statistics, 16(3), 261–272.
Mcleod, A.I. and Hipel, K.W. (1978). Preservation of the rescaled adjusted range, 1: A reassessment of the Hurst phenomenon. Water Resources Research, 14, 491–508.
Sowell, F.B. (1992). Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics, 53, 165–188.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ramachandran, R., Beaumont, P. Robust Estimation of GARMA Model Parameters with an Application to Cointegration among Interest Rates of Industrialized Countries. Computational Economics 17, 179–201 (2001). https://doi.org/10.1023/A:1011640512990
Issue Date:
DOI: https://doi.org/10.1023/A:1011640512990