William R. Parke

WHAT IS FRACTIONAL INTEGRATION

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.

An Algorithm for FIML and 3SLS Estimation of Large Nonlinear Models

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 macroeconomic models. The new algorithm, which is demonstrated by actually computing FIML and 3SLS coefficient estimates for two versions of the 97 equation Fair Model, is substantially more effective than other algorithms on FIML and 3SLS estimation problems.

ASYMPTOTIC LIKELIHOOD BASED PREDICTION FUNCTIONS

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 S. L. Lauritzen (1974) and D. Hinkley (1979). 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 linear-normal models, nonnormal models, and ARCH models. Copyright 1990 by The Econometric Society.

Likelihood and other approaches to prediction in dynamic models

Abstract In this paper we consider the problem of generating multi-period predictions from two simple dynamic models, an autoregressive model and a geometric random walk. The autoregressive model constitutes a useful paradigm for many of the practical problems of prediction because it possesses a number of features that differentiate it sharply from the standard linear regression model. The geometric random walk model is widely used in macroeconomics and finance and is fundamentally non-normal. The ideal situation for the prediction problem would be to know the true density of the future observations. Unfortunately, that density depends on parameters that are unknown and must be estimated. We analyze six prediction functions — approximations of the true density — that attempt to circumvent this problem. We contrast the theoretical properties of the likelihood prediction function proposed by Cooley and Parke (1986) with certainty equivalence prediction functions and mean-squared error prediction functions. The results of a Monte Carlo study illustrate the relative performance of the alternative prediction functions for conditional predictions and for the analysis of policy interventions. The results confirm the importance of accounting for parameter uncertainty and approximating the true shape of the future density.

Predictive efficiency for simple non-linear models

This paper demonstrates the use of exact predictive likelihood functions for simple non-linear models. A measure of predictive efficiency based on the concept of expected information loss is introduced as a way of comparing alternative prediction functions. It is shown that the predictive likelihood function minimizes expected information loss over a wide class of potential prediction functions. Some Monte Carlo experiments illustrate the performance of alternative prediction functions in settings where prediction is difficult.

ON THE EVOLUTIONARY STABILITY OF RATIONAL EXPECTATIONS

Evolutionary game theory provides a fresh perspective on the prospects that agents with heterogeneous expectations might eventually come to agree on a single expectation corresponding to the efficient markets hypothesis. We establish conditions where agreement on a unique forecast is stable, but also show that persistent heterogeneous expectations can arise if those conditions do not hold. The critical element is the degree of curvature in payoff weighting functions agents use to value forecasting performance. We illustrate our results in the context of an asset pricing model where a martingale solution competes with the fundamental solution for agents’ attention.