Initial-Condition-Robust Inference in Autoregressive Models

Donald W. K. Andrews, Ming Li and Yapeng Zheng

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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.

Date: 2026-02, Revised 2026-02
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