Confidence intervals for the largest root of autoregressive models based on instrumental variable estimators

Abstract

For estimating the largest root of autoregressive (AR) models, we propose an instrumental variable scheme which discounts a large value of regressors corresponding to the largest roots. The pivotal value of the estimator of the largest root is asymptotically normal for any value of the largest root. This fact allows us to construct a simple confidence interval based on ±standard error, say, with good coverage probability and shorter average length than those of [J. Monetary Economics, 28, 1991, 435-459] and [Econometrica, 61, 1993, 139-165].