CONFIDENCE INTERVALS FOR ROBUST ESTIMATES OF THE FIRST ORDER AUTOREGRESSIVE PARAMETER

Abstract. The confidence interval properties of several estimators of the transition parameter, φ, in the first order autoregressive model are examined by a Monte Carlo study. The least squares confidence interval estimator, as well as two forms of a proposed robust confidence interval based on a generalized M-estimator, are examined under two model alternatives to the classical time series approach: the innovations model (the time series is observed 'perfectly') and the additive effects model (the time series is observed plus an added 'effect'). Samples were generated from a number of symmetric distributions, including the Gaussian and a variety of contaminated distributions with mild to heavy contamination. Over a range of outlier models, values of φ (.25 to.9), and sample sizes (20 to 100), it was found that the GM-estimators possess desirable confidence interval robustness properties in terms of validity and efficiency. In general, the least squares confidence interval is not robust against symmetric heavy-tailed contamination in the innovations model or against the additive effects model.