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Estimation and inference theory for (co)integrated processes in the state space representation

状态空间表示中（共）积分过程的估计和推理理论

基本信息

批准号：
276051388
负责人：
Professor Dr. Dietmar Bauer, since 10/2019
金额：
--
依托单位：
Lehrstuhl für Ökonometrie
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/276051388?language=en
关键词：
Estimation inference theory co integrated

项目摘要

While estimation and specification theory for (co-)integrated processes is well-studied in the vector-autoregressive (VAR) setting, still little is known about corresponding theory in the framework of vector-autoregressive-moving-average (VARMA) processes and the equivalent state space representation for the empirically relevant integrated processes of order one (l(1)), order two (l(2)), as well as seasonally integrated (MFI(1)) processes. VARMA processes and in particular their state space representation have recently gained a lot of attention in (empirical) macroeconomics due to their strong connection to the solutions of dynamic stochastic general equilibrium (DSGE) models.For the econometric analysis of DSGE models with (co)integrated variables, theory for estimation and inference is needed for state space models with restrictions. Commonly used unrestricted VAR approximations do not encompass the restrictions implied by the models. Furthermore they are not suitable for the analysis of non-invertible systems, which may be problematic for the identification of structural shocks. Moreover, unrestricted VAR systems for models with a large number of endogenous variables entail the need for a large number of parameters which can be substantially reduced with the use of the more flexible class of state space systems. Additionally, the treatment of l(1), l(2), as well as MFI(1) systems eliminates the need for de-trending and de-seasonalizing the data, therefore allowing to incorporate valuable information on the long-run behavior of the variables in the modelling process.Consequently, the main goal of the project is to develop estimation and inference theory which (i) allows to incorporate the restrictions on the dynamic properties of the variables (induced for instance by integration properties and the presence of (polynomial) co-integrating relations), (ii) admits the analysis of non-invertible systems and (iii) optimally exploits the flexibility of state space systems.This goal will be accomplished by (i) developing a parametrization based on the canonical form for unit root processes recently developed by the applicants allowing to incorporate the restrictions induced by economic theory, (ii) deriving asymptotic results for quasi-maximum likelihood estimators for given integer parameters (such as the dimension of the state space) and developing tests for restrictions implied by underlying economic theory, (iii) finding consistent estimators for initializing the maximization of the quasi likelihood function, (iv) defining and thoroughly evaluating algorithms for the specification of integer parameters. Another main achievement is the implementation of the methods in toolboxes (in MATLAB and R). These goals will be achieved by combining the state-space modeling competences of Dietmar Bauer with the profound knowledge on estimation theory and economic application of cointegration analyis of Martin Wagner.

虽然在向量自回归（VAR）环境下对（协）集成过程的估计和规范理论进行了很好的研究，但在向量自回归移动平均（VARMA）过程框架下的相应理论以及经验相关的一阶（l（1））、二阶（l（2））、以及季节性综合（MFI（1））过程。VARMA过程及其状态空间表示由于与动态随机一般均衡（DSGE）模型的解密切相关而在宏观经济学中受到广泛关注，在对具有（协）整变量的DSGE模型进行计量分析时，需要对带约束的状态空间模型进行估计和推断.常用的无限制VAR近似不包含模型隐含的限制。此外，它们不适合于分析不可逆系统，这可能是有问题的结构性冲击的识别。此外，不受限制的VAR系统的模型与大量的内生变量需要大量的参数，可以大大减少与使用更灵活的状态空间系统类。此外，l（1）、l（2）以及MFI（1）系统的处理消除了对数据的去趋势化和去季节化的需要，因此允许在建模过程中并入关于变量的长期行为的有价值的信息。该项目的主要目标是发展估计和推理理论，允许将变量的动态属性的限制（例如由积分性质和（多项式）共积分关系的存在引起），（ii）允许分析不可逆系统和（iii）最佳地利用状态空间系统的灵活性。- 基于申请人最近开发的单位根过程的标准形式开发参数化，允许结合由经济理论引起的限制，（ii）对给定的整数参数，导出拟极大似然估计的渐近结果（如状态空间的维度）和发展测试隐含的基本经济理论的限制，（iii）寻找一致的估计初始化的最大化的准似然函数，（iv）定义和彻底评估算法的规格整数参数。另一个主要成就是在工具箱（MATLAB和R）中实现方法。这些目标将通过将Dietmar Bauer的状态空间建模能力与Martin瓦格纳的估计理论和协整分析的经济应用的深刻知识相结合来实现。