GLASS - The Global Augmented State Space Error Correction Model: Structure Theory, Estimation and Inference

经济和金融一体化程度的提高、大规模（多国）数据集的增加以及高维时间序列计量经济学建模方面的科学进展，导致多国建模取得了重大进展。这些进步发生在经济理论驱动的模型和减少形式的时间序列模型指定使用统计工具，而不是经济理论。对于经验应用，任何考虑中的模型类都必须处理维数灾难，或者换句话说，复杂性降低。在这个项目中，我们的目标是（i）探索和（ii）扩展两个突出的计量经济学方法建模高维（结构化）的时间序列，全球向量自回归（GVAR）和广义动态因子模型（GDFMs）之间的联系。GVAR模型通过严格限制所有其他国家的变量对所考虑的每个国家的变量演变的影响来降低复杂性。其他国家对演化的影响在所谓的星星和全球变量中得到净化。相应的限制一方面取决于许多假定的外生性约束，也限制了建模的灵活性的长期（协整）的联合系统的行为。虽然特别是GVAR模型的“结构形式”可以被视为半结构模型，但GDFMs具有很强的简化形式特征，特别是将系列的共同运动与少数未观察到的和统计上确定的共同因素联系起来。这种方法在降低复杂性方面非常有效，但限制了特定的结构分析和解释。从所有变量都由向量自回归移动平均（VARMA）过程生成的基本假设开始，该项目提出-使用适当的状态空间表示- 全球增广状态空间（GLASS）模型，以（i）解决开放的问题，外生性和协整性质的GVAR型模型在一个模型类，是不变的线性变换和（ii）详细调查（VARMA）GDFMs和GLASS型模型之间的关系。状态空间模型的结构与潜在的（潜在的低维）状态向量描述的动态的可观的是非常相似的结构的GDFMs;提供了研究的关系的切入点。要解决的一个关键问题，以研究跨模型类的链接是一个详细的了解有限N（在GVAR设置）以及N-渐近（GDFMs）的属性和它们之间的相互关系。基于结构理论，GLASS将开发估计和推理工具，允许在高维协整系统中进行结构分析。这些程序和工具将通过经过良好测试和可靠的代码向公众提供。GLASS是我们早期项目EICIP的高维和结构化扩展。

Increased economic and financial integration, increased availability of large-scale (multi-country) data sets and scientific progress in econometric modelling of high-dimensional time series have led to important advances in multi-country modelling. These advances have occurred both in economic theory driven models and reduced form time series models specified using statistical tools rather than economic theory. For empirical application any model class under consideration has to deal with the curse-of-dimensionality or, put differently, complexity reduction. In this project we aim to (i) explore and (ii) extend the linkages between two prominent econometric approaches for modelling high-dimensional (structured) time series, global vector autoregressive (GVAR) and generalized dynamic factor models (GDFMs). GVAR models achieve complexity reduction by strongly restricting the impact of the variables of all other countries on the evolution of the variables in each country considered. The impact of other countries on the evolution is purged in the so-called star and global variables. The corresponding restrictions on the one hand rest upon numerous posited exogeneity constraints and also limit the flexibility of modelling the long-run (cointegration) behavior of the joint system. Whilst in particular “structural forms” of GVAR models can be seen as semi-structural models, GDFMs have a strong reduced form character, relating in particular the co-movements of series to a small number of unobserved and statistically identified common factors. This approach is very efficient in complexity reduction, but limits in particular structural analysis and interpretations.Starting from the underlying assumption that all variables are generated by a vector autoregressive moving average (VARMA) process this project proposes – using appropriate state space representations – the Global Augmented State Space (GLASS) model to (i) address open issues with respect to exogeneity and cointegration properties in GVAR-type models in a model-class that is invariant to linear transformations and (ii) to investigate in detail the relationship between (VARMA) GDFMs and GLASS-type models. The structure of state space models with the latent (potentially low-dimensional) state vector describing the dynamics of the observables is very similar to the structure of GDFMs; providing the entry point for studying the relationships. A key issue to be addressed to study the links across model classes is a detailed understanding of both finite-N (in GVAR settings) as well as N-asymptotic (GDFMs) properties and their interrelationships. Based upon the structure theory, GLASS will develop estimation and inference tools allowing for structural analysis in high-dimensional cointegrated systems. The procedures and tools will be made available to the public by means of well-tested and robust code. GLASS is a high-dimensional and structural extension of our earlier project EICIP.