A comparison between behavioral similarity methods vs standard deviation method in predicting time series dataset, case study of finance market

TL;DR

This study compares traditional standard deviation-based confidence intervals with similarity-based methods in time series forecasting of financial data, highlighting trade-offs between interval width and coverage for different approaches.

Contribution

It provides an empirical comparison of traditional and similarity-based confidence interval methods in financial time series prediction, emphasizing their relative accuracy and coverage.

Findings

Variance-based and LCSS methods have highest coverage but broader intervals.

DTW, Hausdorff, and TWED produce narrower intervals with medium coverage.

Trade-offs exist between interval precision and coverage, requiring context-aware method selection.

Abstract

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 variance 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.