Initial-Condition-Robust Inference in Autoregressive Models

2026-02-10

AI Summary

This study addresses the severe undercoverage of conventional confidence intervals for parameters in autoregressive models when the process is nonstationary or initialized under unknown conditions. To resolve this issue, the authors propose a novel method for constructing confidence intervals that is fully robust to arbitrary initial conditions. Grounded in robust statistical inference theory, the approach integrates asymptotic distributional analysis of autoregressive processes with heteroskedasticity-robust techniques. The resulting intervals achieve the nominal coverage probability uniformly across all initial conditions and maintain robustness against conditional heteroskedasticity in the error terms. Moreover, in stationary settings, the proposed intervals incur virtually no efficiency loss in length compared to standard methods, thereby offering a significant improvement over existing approaches.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• autoregressive model
• confidence interval
• initial condition
• unit root
• coverage probability

Innovation

• initial-condition robustness
• autoregressive models
• confidence intervals
• conditional heteroskedasticity
• finite-sample coverage