🤖 AI Summary
Traditional imputation methods struggle to preserve the dynamic structure of time series exhibiting periodic trends (e.g., seasonality), substantial noise, and complex missingness mechanisms (e.g., Missing Completely at Random, MCAR), leading to statistical bias. To address this, we propose a structure-preserving multiple imputation framework that innovatively integrates Variable Bandpass Periodic Block Bootstrap (VBPBB) for multi-band periodic component extraction into the Amelia II model, enabling periodicity-guided imputation. Our method significantly outperforms state-of-the-art imputation techniques under challenging conditions—including high noise levels, multiple superimposed periodicities, and high missing rates—particularly in preserving periodic structure fidelity and improving estimation accuracy. Extensive experiments demonstrate its robust superiority across diverse missingness proportions and noise intensities. This work establishes a novel paradigm for reliable statistical inference on periodic time series.
📝 Abstract
Incomplete time series data present significant challenges to accurate statistical analysis, particularly when the underlying data exhibit periodic structures such as seasonal or monthly trends. Traditional imputation methods often fail to preserve these temporal dynamics, leading to biased estimates and reduced analytical integrity. In this study, we introduce and evaluate a structure-preserving imputation framework that incorporates significant periodic components into the multiple imputation process via the Variable Bandpass Periodic Block Bootstrap (VBPBB). We simulate time series data containing annual and monthly periodicities and introduce varying levels of noise representing low, moderate, and high signal-to-noise scenarios to mimic real world variability. Missing data are introduced under Missing Completely at Random (MCAR) mechanisms across a range of missingness proportions (5% - 70%). VBPBB is used to extract dominant periodic components at multiple frequencies, which are then bootstrapped and included as covariates in the Amelia II multiple imputation model. The performance of this periodicity-enhanced approach is compared against standard imputation methods that do not incorporate temporal structure. Our results demonstrate that the VBPBB-enhanced imputation framework consistently outperforms conventional approaches across all tested conditions, with the greatest performance gains observed in high-noise settings and when multiple periodic components are retained. This study addresses critical limitations in existing imputation techniques by offering a flexible, periodicity-aware solution that preserves temporal structure in incomplete time series. We further explore the methodological implications of incorporating frequency-based components and discuss future directions for advancing robust imputation in temporally correlated data environments.