Estimation, Inference, and Empirical Analysis for Time-Varying VAR Models

Vector autoregressive (VAR) models are widely used in practical studies, for example, forecasting, modeling policy transmission mechanism, and measuring connection of economic agents. To better capture the dynamics, this article introduces a new class of time-varying VAR models in which the coefficients and covariance matrix of the error innovations are allowed to change smoothly over time. Accordingly, we establish a set of asymptotic properties including the impulse response analyses subject to structural VAR identification conditions, an information criterion to select the optimal lag, and a Wald-type test to determine the constant coefficients. Simulation studies are conducted to evaluate the theoretical findings. Finally, we demonstrate the empirical relevance and usefulness of the proposed methods through an application on U.S. government spending multipliers.

向量自回归（Vector Autoregressive, VAR）模型在实际研究中应用广泛，可用于预测、政策传导机制建模以及测度经济主体间的关联。为更好地捕捉序列动态特征，本文提出一类新型时变向量自回归（VAR）模型，其中模型系数与误差扰动项的协方差矩阵可随时间平滑变化。据此，本文构建了一系列渐近性质，包括满足结构VAR识别条件的脉冲响应分析、用于选取最优滞后阶数的信息准则，以及用于检验系数是否为常数的沃尔德型检验。本文通过模拟实验对上述理论结论进行了验证。最后，本文通过美国政府支出乘数的实证应用，展示了所提方法的实证适用性与应用价值。