Back To Index Previous Article Next Article Full Text Supplement


Statistica Sinica 19 (2009), 1263-1280





ROBUST TIME SERIES ANALYSIS VIA

MEASUREMENT ERROR MODELING


Qiong Wang$^1$, Leonard A. Stefanski$^2$, Marc G. Genton$^{3,4}$ and Dennis D. Boos$^2$


$^1$GlaxoSmithKline, $^2$North Carolina State University, $^3$University of Geneva
and $^4$Texas A$\&$M University



Abstract: 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.

Key words and phrases: Bayesian inference, error contamination model, influence function, measurement error, MCMC, robustness.

Back To Index Previous Article Next Article Full Text Supplement