Efficient Detection and Estimation of Multiple Structural Breaks in Cointegrated Systems

结构突变建模是时间序列分析中的一个重要课题。结构突变的数量、发生的时间和强度通常是未知的，必须根据数据进行估计。一系列新的文献在惩罚回归的背景下应用最先进的方法来解决变点问题。他们认为检测和估计线性回归中的结构突变的任务是一个模型选择问题。例如，原则上，LASSO估计量在这些设置中具有吸引人的特性。它的目标函数包括非零参数的惩罚和调整参数控制所选模型的稀疏性。然而，在变点设置中，我们知道如果样本量变大并且LASSO不再是模型选择一致的，则设计矩阵可以是高度共线的。因此，多步估计过程是必要的，以清除多余的断点候选人的模型。框架的变点问题作为一个模型选择问题的背景下，惩罚回归允许研究人员应用众所周知的方法和算法，从不同领域的高维回归分析，提供了高的灵活性和计算效率。这一方法的另一个积极方面是，可以用很少的额外计算成本来捕捉多个结构性突变，这一研究方案的重点是对经济变量之间长期均衡关系中的结构性变化进行统计建模。更确切地说，我们考虑向量误差校正模型和多方程协整回归中的结构突变。我们集中在以下重要问题，即估计（i）在协整系统的结构性突变的数量，（ii）他们的时间，（iii）他们的大小。由于协整模型涉及集成回归，在这种情况下，结构突变估计的渐近理论预计是非标准的，并提供了一些计量经济学的挑战。因此，我们的目标之一是发展这些估计的渐近理论。在项目1中，我们将单方程协整模型中的（自适应）组LASSO估计的结果推广到多方程协整系统。这种推广使我们能够有效地模型的协整系统，保持一个以上的长期平衡，并涵盖额外的实证applications.In项目2，我们使用惩罚回归方法来解决变点问题的向量误差校正模型的结构不稳定。在这里，我们的目标是检测和估计长期系数中的多个结构性突变，而不对协整方向进行归一化。这种方法的另一个特点是能够检测调整速度的变化，使用项目1中提出的方法，调整速度假定为恒定。

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.