Document Type
Discussion Paper
Publication Date
2-2026
CFDP Number
2496
CFDP Pages
47
Journal of Economic Literature (JEL) Code(s)
C10, C12
Abstract
This paper considers confidence intervals (CIs) for the autoregressive (AR) parameter in an AR model with an AR parameter that may be close or equal to one. Existing CIs rely on the assumption of a stationary or fixed initial condition to obtain correct asymptotic coverage and good finite sample coverage. When this assumption fails, their coverage can be quite poor. In this paper, we introduce a new CI for the AR parameter whose coverage probability is completely robust to the initial condition, both asymptotically and in finite samples. This CI pays only a small price in terms of its length when the initial condition is stationary or fixed. The new CI also is robust to conditional heteroskedasticity of the errors.
Recommended Citation
Andrews, Donald W. K.; Li, Ming; and Zheng, Yapeng, "Initial-Condition-Robust Inference in Autoregressive Models" (2026). Cowles Foundation Discussion Papers. 2929.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2929