Exact Maximum Likelihood Estimation of Fractional Models and Time Series Nature of the Real GNP of Korea

An exact maximum likelihood estimation algorithm for estimating univariate ARFIMA(17, d, q) model is suggested. The transformation method based on Cholesky decomposition is useful in that it can easily incorporate well-established techniques of estimating ARMAHL q) model and also avoids the problems of Sowell (1992a). For the development of an exact maximum likelihood estimation method that is used throughout the study. the algorithm of Ansley(1979) for general ARMA(p, q) model is incoiporated. A small simulation shows that any one of maximum likelihood estimation method and the method of Li and McLeod(1986) does not clearly dominate the other in precision and dispersion, although the latter has known truncation problem, in the samples of length 100. The performances of maximum likelihood estimation when the ruefractional differencing parameter is close to the boundary of 0.5 are relatively poor, however that can be improved by reparameterizing d. Estimating ARFIMA models by exact maximum likelihood method developed in this studv, a time series nature of quarterly real GNP series of Korea is analyzed. When two intervention variables are introduced under the assumption of known events, all three types of the models, deterministic trend model. stochastic trend model, and more general fractional model, seem to estimate the series reasonably well. However, the likelihood ratio test and spectral analysis show that the stochastic trend representations appear to be less adequate in capturing the low frequency behavior of GNP than fractional representations and deterministic trend representations.