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.

A review of probabilistic methods of assessment of load effects in bridges

“…Cooley and Parke have a number of papers dealing with the prediction issue (Cooley & Parke, 1987, Cooley & Parke, 1990, Cooley et al, 1989. However, their method relies on the assumption that the parameters are normally distributed.…”