Missing Data Substitution for Enhanced Robust Filtering and Forecasting in State-Space Models

Replacing erroneous observations with missing values is known to mitigate outlier-induced distortions in state-space model inference. Yet, in economic data, outliers can be small and difficult to detect, while still occurring in temporal clusters and generating persistent distortions. We therefore put forward an unsupervised approach for exogenously randomized substitution of missing data (RMDX), designed as an ensemble-averaging enhancement that can be used to improve the robustness of any filter also to more elusive outliers. Our bias-variance decomposition theory for RMDX ensemble averaging establishes that, under mild regularity conditions on the influence of outliers, the missing data randomization rate acts as a regularization parameter, which can be set optimally to minimize mean squared error loss using standard cross-validation. We corroborate these theoretical results using Monte Carlo simulations, which show that RMDX ensemble averaging can substantially enhance the performance of commonly used robust filters, including ones that rely on supervised missing data substitution upon exceeding outlier detection thresholds. As anticipated, the gains are most pronounced in the presence of patches of moderately sized outliers that are difficult to mitigate. To further assess empirical relevance in economics, we also document that RMDX-enhanced filters perform favorably in widely used state-space models for extracting inflation trends, where clusters of measurement outliers in inflation data are known to pose an extra challenge.