Missing Data Treatment in Interval-Valued Time Series via Interval Penalty Functions

P. Huidobro Fernández, A. Bouchet, S. Diaz-Vazquez, S. Montes

Interval-valued time series arise when each observation is represented by an interval capturing variability or uncertainty. Handling missing data in this context is a fundamental challenge, as most imputation methods are designed for precise (point-valued) observations.

We propose a novel framework based on interval penalty functions that operates directly in the interval domain. Missing observations are estimated by selecting the interval that minimizes the maximum discrepancy with respect to neighboring intervals, ensuring coherence and consistency of the reconstructed series. Different distance measures and neighborhood strategies are analyzed within this framework.

Experimental results on simulated data under MCAR, MAR, and MNAR show that the approach is competitive with classical smoothing techniques and often outperforms standard methods in structured and seasonal scenarios, highlighting its flexibility and effectiveness.

Keywords: Interval-valued time series, missing data imputation, interval penalty functions, interval data.

Time Series
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