A Structure-Preserving Assessment of VBPBB for Time Series Imputation Under Periodic Trends, Noise, and Missingness Mechanisms

TL;DR

This paper introduces a structure-preserving multiple imputation method for time series data with periodic trends, noise, and missingness, improving accuracy by incorporating frequency-specific information via VBPBB.

Contribution

It proposes a novel framework that enhances imputation accuracy by integrating frequency-specific covariates derived from VBPBB, specifically addressing periodic structures in time series.

Findings

VBPBB-enhanced imputation reduces error compared to baseline methods.

Incorporating multiple periodic components improves reconstruction under high noise.

Method effectively preserves seasonal signals even with high missingness.

Abstract

Incomplete time-series data compromise statistical inference, particularly when the underlying process exhibits periodic structure (e.g., annual or monthly cycles). Conventional imputation procedures rarely account for such temporal dependence, leading to attenuation of seasonal signals and biased estimates. This study proposes and evaluates a structure-preserving multiple imputation framework that augments imputation models with frequency-specific covariates derived via the Variable Bandpass Periodic Block Bootstrap (VBPBB). In controlled simulations, we generate series with annual and monthly components, impose Gaussian noise across low, moderate, and high signal-to-noise regimes, and introduce Missing Completely at Random (MCAR) patterns from 5% to 70% missingness. Dominant periodic components are extracted with VBPBB, resampled to stabilize uncertainty, and incorporated as covariates in Amelia II. Compared with baseline methods that do not model temporal structure, the VBPBB-enhanced approach consistently yields lower imputation error and superior retention of periodic features, with the largest gains observed under high noise and when multiple components are included. These findings demonstrate that explicitly modeling periodic content during imputation improves reconstruction accuracy and preserves time-series structure in the presence of substantial missingness.