In statistical modeling, prediction and explanation are two fundamental objectives. When the primary goal is forecasting, it is important to account for the inherent uncertainty associated with estimating unknown outcomes. Traditionally, confidence intervals constructed using standard deviations have served as a formal means to quantify this uncertainty and evaluate the closeness of predicted values to their true counterparts. This approach reflects an implicit aim to capture the behavioral similarity between observed and estimated values. However, advances in similarity-based approaches present promising alternatives to conventional variance-based techniques, particularly in contexts characterized by large datasets or a high number of explanatory variables. This study aims to investigate which methods—either traditional or similarity-based—are capable of producing narrower confidence intervals under comparable conditions, thereby offering more precise and informative intervals. The dataset utilized in this study consists of U.S. mega-cap companies, comprising 42 firms. Due to the high number of features, interdependencies among predictors are common; therefore, Ridge Regression is applied to address this issue. The research findings indicate that the σ-based method and LCSS exhibit the highest coverage among the analyzed methods, although they produce broader intervals. Conversely, DTW, Hausdorff, and TWED deliver narrower intervals, positioning them as the most accurate methods, despite their medium coverage rates. Ultimately, the trade-off between interval width and coverage underscores the necessity for context-aware decision-making when selecting similarity-based methods for confidence interval estimation in time series analysis.
Mahdi Goldani (Wed,) studied this question.