THIS PAPER PRESENTS a numerical algorithm for computing full information maximum likelihood (FIML) and nonlinear three-stage least squares (3SLS) coefficient estimates for large nonlinear models. (The proposed algorithm will be denoted algorithm A.) Although the theory of FIML estimation has been available for thirty years [20], FIML estimation has long been regarded as impossible on large nonlinear models.2 The more recently proposed nonlinear 3SLS estimator [191 also poses difficulties for large models.3 Using the algorithm presented in this paper, FIML and 3SLS are now feasible alternatives for estimation of large nonlinear models. The principles behind algorithm A's efficiency can be summarized as follows. First, most of the algorithm's steps explicitly control the mean of each equation's residuals. Large changes in those means are avoided because the FIML and 3SLS estimation problems are extremely sensitive to the residuals' means. Second, the coefficients are grouped by equations and the groups are treated separately during most of each iteration. This focus on individual equations is effective because coefficients within the same equation are generally more

A simple construction that will be referred to as an error-duration model is shown to generate fractional integration and long memory. An error-duration representation also exists for many familiar ARMA models, making error duration an alternative to autoregression for explaining dynamic persistence in economic variables. The results lead to a straightforward procedure for simulating fractional integration and establish a connection between fractional integration and common notions of structural change. Two examples show how the error-duration model could account for fractional integration in aggregate employment and in asset price volatility.

This paper develops asymptotic prediction functions that approximate the shape of the density of future observations and correct for parameter uncertainty. The functions are based on extensions to a definition of predictive likelihood originally suggested by Lauritzen and Hinkley. The prediction function is shown to possess efficiency properties based on the Kullback-Leibler measure of information loss. Examples of the application of the prediction function and the derivation of relative efficiency are shown for linearnormal models, nonnormal models, and ARCH models.

economic models ; financial market ; tests