发表机构
Maastricht University（马斯特里赫特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为矩阵自回归模型的脉冲响应提出渐近与自举推断方法，并引入偏差校正的ProBAB-MAR自举，在小样本中实现更准确的覆盖率和更窄的置信区间，应用于欧元区通胀传导分析。
AI 中文摘要
矩阵自回归（MAR）模型为建模矩阵值时间序列提供了一个简约的框架，然而针对其脉冲响应函数的估计与推断工具尚属缺乏。我们为稳定的MAR($p$)模型的脉冲响应开发了渐近和基于自举的推断方法。我们推导了系数和协方差估计量的联合渐近分布，从而允许使用闭式德尔塔法标准误差。为解决有限样本偏差，我们提出了ProBAB-MAR，一种偏差校正的自举方法，该方法将校正后的系数投影回Kronecker参数空间，并证明其能达到渐近正确的覆盖率。蒙特卡洛模拟表明，德尔塔法区间在小样本中覆盖不足，而ProBAB-MAR实现了接近名义覆盖率，且区间比无约束VAR的区间窄得多。对欧元区通胀的应用说明了冲击如何跨国和跨通胀类别传导。
英文摘要
Matrix autoregressive (MAR) models offer a parsimonious framework for modeling matrix-valued time series, yet tools for estimation and inference for their impulse response functions are lacking. We develop asymptotic and bootstrap-based inference for impulse responses of stable MAR($p$) models. We derive the joint asymptotic distribution of the coefficient and covariance estimators, which permits closed-form delta-method standard errors. To address finite-sample bias, we propose ProBAB-MAR, a bias-corrected bootstrap that projects the corrected coefficients back onto the Kronecker parameter space, and prove that it attains asymptotically correct coverage. Monte Carlo simulations show that delta-method intervals undercover in small samples, while ProBAB-MAR achieves near-nominal coverage with intervals considerably narrower than those from an unrestricted VAR. An application to euro area inflation illustrates how shocks transmit across countries and inflation categories.
Comments29 pages + 30 pages appendix, 8 figures, 1 table
