可能不可逆SVARMA模型的可辨识性与估计：一种新的参数化方法
Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation
摘要：
本文讨论了独立和非高斯冲击驱动的可能不可逆的结构向量自回归移动平均（SVARMA）模型的参数化，可识别性和最大似然（ML）估计。与以前的文献相比，MA多项式矩阵使用维纳-霍普夫分解（WHF）的新表示侧重于模型的多变量性质，生成对其结构的见解，并使用此结构设计优化算法。特别地，它允许参数化单位圆内部和外部的行列式零点的位置，并且它允许MA零点为零，这可以被解释为信息延迟。这与动态随机一般均衡（DSGE）模型的数据驱动评估高度相关。通常对激波传递矩阵以及行列式根位置施加的识别限制是可检验的。此外，我们提供了低水平的条件，渐近正态性的ML估计和分析表达式的得分和信息矩阵。作为应用，我们估计布兰查德和夸模型，并表明我们的方法提供了进一步的见解，使用标准的宏观计量经济模型的不可逆性。这些和进一步的分析是在一个有据可查的R包中实现的。
英文摘要：
This article deals with parameterisation, identifiability, and maximum likelihood (ML) estimation of possibly non-invertible structural vector autoregressive moving average (SVARMA) models driven by independent and non-Gaussian shocks. In contrast to previous literature, the novel representation of the MA polynomial matrix using the Wiener-Hopf factorisation (WHF) focuses on the multivariate nature of the model, generates insights into its structure, and uses this structure for devising optimisation algorithms. In particular, it allows to parameterise the location of determinantal zeros inside and outside the unit circle, and it allows for MA zeros at zero, which can be interpreted as informational delays. This is highly relevant for data-driven evaluation of Dynamic Stochastic General Equilibrium (DSGE) models. Typically imposed identifying restrictions on the shock transmission matrix as well as on the determinantal root location are made testable. Furthermore, we provide low level conditions for asymptotic normality of the ML estimator and analytic expressions for the score and the information matrix. As application, we estimate the Blanchard and Quah model and show that our method provides further insights regarding non-invertibility using a standard macroeconometric model. These and further analyses are implemented in a well documented R-package.
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