Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR(∞) Models*
证明了在数据生成过程可能为无限阶VAR时，对有限阶VAR模型拟合后的斜率参数与创新方差平滑函数进行残差自助法的渐近有效性，适用于预测力、脉冲响应等统计量，无需方差闭合解。
It is common to conduct bootstrap inference in vector autoregressive (VAR) models based on the assumption that the underlying data‐generating process is of finite‐lag order. This assumption is implausible in practice. We establish the asymptotic validity of the residual‐based bootstrap method for smooth functions of VAR slope parameters and innovation variances under the alternative assumption that a sequence of finite‐lag order VAR models is fitted to data generated by a VAR process of possibly infinite order. This class of statistics includes measures of predictability and orthogonalized impulse responses and variance decompositions. Our approach provides an alternative to the use of the asymptotic normal approximation and can be used even in the absence of closed‐form solutions for the variance of the estimator. We illustrate the practical relevance of our findings for applied work, including the evaluation of macroeconomic models.