Prediction Intervals for Non-Negative Series

• Activity Number: 441
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Keith Ord*+
• Companies: Georgetown Univ
• Keywords: Forecasting ; Co-integration ; State space models

Abstract

When a non-negative time series is stable but not mean-reverting, theory indicates that it will ultimately increase without limit or that it will converge almost surely to zero. In practice, neither of these situations is typical, although companies do go bankrupt and consumers turn away from established products. In this paper we propose a model with a hidden cointegrated variable that is able to represent both these forms of behavior and situations of mean or trend-reverting behavior. An implication of these results is that model-based prediction intervals may be seriously biased for longer lead-times and intervals should be estimated empirically whenever possible. Data on daily closing prices of the Dow Jones Index are used to illustrate the results.