Robust time series analysis via measurement error modeling

We describe an approach for robustifying inference in parametric models that is attractive for time series models. The key feature is that data from the postulated models are assumed to be measured with sporadic gross errors. We show that the tails of the error-contamination model kernel control the influence function properties (unbounded, bounded, redescending), with heavier tails resulting in greater robustness. The method is studied first in location-scale models with independent and identically distributed data, allowing for greater theoretical development. In the application to time series data, we propose a Bayesian approach and use Markov chain Monte Carlo methods to implement estimation and obtain outlier diagnostics. Simulation results show that the new robust estimators are competitive with established robust location-scale estimators, and perform well for ARMA (p,q) models.