Subsampling intervals in (un)stable autoregressive models with stationary covariates

This paper considers confidence intervals based on the subsampling approach for the largest root in possibly unstable AR(p) models with stationary exogenous regressors. The subsampling approach proposed by Politis and Romano (Annals of Statistics, 1994), is able to deal with discontinuities in the asymptotic distribution of a (studentized) estimator. We show that inference based on subsampling intervals is asymptotically correct. The finite-sample behavior of the subsampling approach is investigated by a small simulation study. It turns out that an equal-tailed subsampling interval based on a calibration rule leads to accurate inference in samples of size 100.