One-Dimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root
研究了在可能存在单位根的自回归模型中，如何对系数的一维函数（如脉冲响应）进行检验和置信区间构建，提出了新的渐近框架并改进了已有方法。
This paper examines the problem of testing and confidence set construction for one-dimensional functions of the coefficients in autoregressive (AR(p)) models with potentially persistent time series. The primary example concerns inference on impulse responses. A new asymptotic framework is suggested and some new theoretical properties of known procedures are demonstrated. I show that the likelihood ratio (LR) and LR± statistics for a linear hypothesis in an AR(p) can be uniformly approximated by a weighted average of local-to-unity and normal distributions. The corresponding weights depend on the weight placed on the largest root in the null hypothesis. The suggested approximation is uniform over the set of all linear hypotheses. The same family of distributions approximates the LR and LR± statistics for tests about impulse responses, and the approximation is uniform over the horizon of the impulse response. I establish the size properties of tests about impulse responses proposed by Inoue and Kilian (2002) and Gospodinov (2004), and theoretically explain some of the empirical findings of Pesavento and Rossi (2007). An adaptation of the grid bootstrap for impulse response functions is suggested and its properties are examined.