Enhancing data completeness in time series: Imputation strategies for missing data using significant periodically correlated components

Abstract

Missing data in periodic time series can bias inference when temporal dependence is not preserved during imputation. We propose a framework that integrates the Variable Bandpass Periodic Block Bootstrap (VBPBB) with multiple imputation using Amelia II by incorporating statistically significant periodic components as auxiliary covariates. Performance was evaluated using simulated missingness in temperature time series data with seasonal structure under a Missing at Random (MAR) mechanism. Imputation accuracy was assessed using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), comparing Amelia II models with and without VBPBB-derived periodic covariates. Incorporating periodic components reduced RMSE and MAE by approximately 55%, indicating improved reconstruction of seasonal patterns. These results suggest that preserving periodic dependence can enhance imputation performance in time series with strong seasonal structure.