Forecasting from fallible data: Correcting prediction bias with stein-rule least squares
✍ Scribed by T. D. Stanley
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 685 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0277-6693
No coin nor oath required. For personal study only.
✦ Synopsis
In the presence of fallible data, standard estimation and forecasting techniques are biased and inconsistent. Surprisingly, the magnitude of this bias tends to increase, arid not diminish, in time series applications as more observations become available. A solution to this ever-present problem, Stein-rule least squares (SRLS), is offered. It corrects for the bias and inconsistency of traditional estimators and provides a means for significantly improving the predictive accuracy of regression-based forecasting techniques. A Monte Carlo study of the forecasting accuracy of SRLS, compared to its alternatives reveals its practical significance and small sample behaviour.
K E Y WORDS Errors-in-variables Fallible data Stein-rule estimation
Reliability Monte Carlo study.
'Aboul [he best an applied researcher can do is recognize that the data being used are likely to be affcted with errors, examine to the extent possible the implications of the errorsfor the analysis, and assume an attitude of humility when druwing conclusions based on the sample'. (Johnson, Johnson and Buse, 1987, p. 327) I t is perhaps trite to suggest that our predictions are only as good as the models from which they are derived. However, less attention is paid to the equally important connection between the quality of our forecasting models and the reliability of the data used in their estimation. I t is generally known that the fallibility of our data (called 'errors-in-variables' or 'unobservable variables') causes the traditional regression estimation procedure, ordinary least squares (OLS), to be biased and inconsistent-for example, Theil (1971). The implications of this problem, however, go beyond regression and econometric modelling and apply to regression-based and regression-like forecasting techniques, such as exponential smoothing and ARIMA models (Brown, 1963, Friedman and Montgomery 1985). The purpose of this paper is to discuss Stein-rule least squares as a resolution to difficulties which result from fallible data and to evaluate the predictive accuracy of alternative regression estimators when o u r data are less than perfect.