Adaptive Estimation: An Alternative to the Traditional Stationarity Assumption

Abstract

There have been many studies dealing with forecasting future accounting earnings using quarterly data (e.g., Lorek [1979], Brown and Rozeff [1979], and Foster [1977]). Most of these studies use a Box-Jenkins (BJ) methodology in formulating their predictions. One of the major problems with the BJ methodology is the assumption that the underlying structure is stable over time. In this paper, I examine whether a model that adapts its structure to the changing nature of time-series data can outpredict a BJ model which assumes stationary coefficients. If the time-series structure of eps is nonstationary, one would expect the AEP model to outpredict the other models used. Since it cannot be shown analytically that accounting series are nonstationary, this study should be considered exploratory. As an additional benchmark I also compare predictions of the BJ model to a regression model and a simple random walk model. The set of models used here will be identified as follows: (1) Ordinary Least Squares (OLS), (2) Firm-Specific Box-Jenkins (FBJ), (3) Parsimonious Box-Jenkins (PBJ), (4) Industry Parsimonious Box-Jenkins (IPBJ), (5) Adaptive Estimation Parameter (AEP), and (6) Random Walk (RW). The forecasts are made over three different time horizons