Robust outlier-adjusted mean-shift estimation of state-space models

TL;DR

ROAMS is a robust estimation method for state-space models that effectively detects and adjusts for outliers, leading to more reliable parameter estimates in contaminated time series data.

Contribution

This paper introduces ROAMS, a novel outlier-adjusted estimation approach for state-space models that combines outlier detection with parameter estimation in a unified framework.

Findings

ROAMS outperforms classical methods in robustness on simulated data.

ROAMS provides reliable estimates on real-world animal tracking data.

Diagnostic tools like BIC curves aid in tuning and outlier visualization.

Abstract

State-space models (SSMs) provide a flexible framework for modelling time series data, but their reliance on Gaussian error assumptions makes them highly sensitive to outliers. We propose a robust estimation method, ROAMS, that mitigates the influence of additive outliers by introducing shift parameters at each timepoint in the observation equation of the SSM. These parameters allow the model to attribute non-zero shifts to outliers while leaving clean observations unaffected. ROAMS then enables automatic outlier detection, through the addition of a penalty term on the number of flagged outlying timepoints in the objective function, and simultaneous estimation of model parameters. We apply the method to robustly estimate SSMs on both simulated data and real-world animal location-tracking data, demonstrating its ability to produce more reliable parameter estimates than classical methods and other benchmark methods. In addition to improved robustness, ROAMS offers practical diagnostic tools, including BIC curves for selecting tuning parameters and visualising outlier structure. These features make our approach broadly useful for researchers and practitioners working with contaminated time series data.