Assessing the Relationship Between Prediction Intervals and Confidence Intervals in Statistical Forecasting

Posted: Nov 17, 1994

• Ryan Long
• William Gray
• Abigail Turner

Abstract

Statistical forecasting represents a cornerstone of quantitative analysis across numerous disciplines, from economics and finance to environmental science and public health. The accurate quantification of forecast uncertainty stands as an equally important endeavor as point forecasting itself, as decision-makers increasingly rely on probabilistic assessments to navigate complex, uncertain environments. Within this context, two distinct but often conflated concepts emerge: prediction intervals and confidence intervals. While both serve as measures of uncertainty, their conceptual foundations, computational methodologies, and interpretative frameworks differ fundamentally. Prediction intervals provide a range within which future observations are expected to fall with a specified probability, accounting for both parameter uncertainty and inherent variability in the data generating process. In contrast, confidence intervals quantify the uncertainty surrounding parameter estimates, reflecting the precision with which these parameters have been estimated from the available sample. The distinction, while theoretically clear, becomes blurred in practical forecasting applications, where confidence intervals are frequently employed as surrogates for prediction intervals due to computational convenience or conceptual misunderstanding. This paper addresses a critical gap in the forecasting literature by systematically examining the relationship between prediction intervals and confidence intervals across diverse statistical environments. We challenge the prevailing assumption that confidence intervals can adequately substitute for prediction intervals in forecasting contexts, particularly when the underlying data generating process exhibits complex dynamics such as heteroscedasticity, structural breaks, or non-stationarity.