Efficient Detection and Estimation of Multiple Structural Breaks in Cointegrated Systems

构造突变模型是时间序列分析中的一个重要课题。结构突变的数量、时间和规模通常是未知的，必须从数据中估计出来。一种新的文学流派将最先进的方法应用于惩罚回归的背景下，以解决变点问题。他们将检测和估计线性回归中的结构突变视为模型选择问题。例如，套索估计器原则上在这些设置下具有诱人的性质。它的目标函数包括对非零参数的惩罚和控制所选模型的稀疏性的调整参数。然而，在变点设置中，我们知道，如果样本大小变大，套索不再是模型选择的一致性，则设计矩阵可以高度共线。因此，从多余的断点候选中清除模型的多步估计过程是必要的。在惩罚回归的背景下，将变点问题框架化为模型选择问题，允许研究人员应用高维回归分析中各种领域的著名方法和算法，这些方法和算法具有很高的灵活性和计算效率。这种方法的另一个积极方面是，可以在几乎不增加计算成本的情况下捕捉多个结构突变。这一研究计划的重点是对经济变量之间长期均衡关系中的结构变化进行统计建模。更准确地说，我们考虑了向量误差修正模型和多元方程协整回归中的结构性突变。我们集中在以下重要问题上，即估计(I)协整系统中结构突变的数量，(Ii)它们的时机，以及(Iii)它们的大小。由于协整模型涉及集成回归变量，在这种情况下结构突变估计量的渐近理论预计将是非标准的，并提供了几个计量经济学挑战。因此，我们的目标之一是发展这些估计量的渐近理论。在项目1中，我们将单方程协整模型中(自适应)组LASSO估计量的结果推广到多方程协整系统。这一推广使我们能够有效地对保持一个以上长期均衡的协整系统的结构不稳定性进行建模，并涵盖其他经验应用。在项目2中，我们使用惩罚回归方法来解决向量误差修正模型中的变点问题。在这里，我们的目标是在不对协整方向施加归一化的情况下检测和估计长期系数中的多个结构突变。这种方法的另一个特点是能够利用项目1中提出的方法发现调整速度的变化，该速度假定是恒定的。

Modelling structural breaks is an important topic in time series analysis. The number of structural breaks, their timing, and their magnitude are usually unknown and must be estimated from the data. A new strand of literature applies state-of-the-art methods in the context of penalized regressions to tackle change-point problems. They view the task of detecting and estimating structural breaks in linear regressions as a model selection problem. For instance, the LASSO estimator, in principle, has attractive properties in those settings. Its objective function includes a penalty for nonzero parameters and a tuning parameter controls the sparsity of the selected model. However, in change-point settings, we know that the design matrix can be highly collinear if the sample size grows large and LASSO is no longer model selection consistent. Hence, multiple-step estimation procedures are necessary to purge the model from superfluous breakpoint candidates. Framing the change-point problem as a model selection problem in the context of penalized regressions allows researchers to apply well-known methods and algorithms from the diverse field of high-dimensional regression analysis which provide both high flexibility and computational efficiency. Another positive aspect of this approach is the possibility of capturing multiple structural breaks with little additional computational costs.The focus of this research programme is on the statistical modelling of structural change in long-run equilibrium relationships between economic variables. More precisely, we consider structural breaks in vector error correction models and multiple equation cointegrating regressions. We concentrate on the following important issues, namely estimating (i) the number of structural breaks in cointegrated systems, (ii) their timing, and (iii) their magnitude. Since cointegration models involve integrated regressors, the asymptotic theory for structural break estimators in this context is expected to be nonstandard and provides several econometric challenges. Hence, one of our goals is to develop the asymptotic theory for those estimators.In Project 1, we will extend the results obtained for (adaptive) group LASSO estimators in single equation cointegration models to multiple equation cointegrated systems. This generalization allows us to efficiently model structural instability in cointegrated systems that maintain more than one long-run equilibrium and covers additional empirical applications.In Project 2, we use the penalized regression approach to solve change-point problems in vector error correction models. Here, we aim to detect and estimate multiple structural breaks in the long-run coefficients without imposing a normalization on the cointegrating directions. Another feature of this approach is the ability to detect changes in the speed of adjustment which is assumed to be constant using the methodology proposed in Project 1.