The effect of structural changes to inference in long-memory time series

第二个项目阶段的动机是Bertram，Kruse和Sibbertsen（2013）的工作，他们发现了美国股票收益率实现相关性的长期依赖性和结构性突变。此外，断裂似乎发生在相同的时间点。这种经验规律性提出了几个研究问题：首先，在数据中发现的长期依赖性可能是由于结构变化。因此，需要一种多变量算法来测试结构突变，并且对长记忆具有鲁棒性。其次，结构突变的相同时间点可能表明时间序列之间存在共突变关系。然而，Hendry & Massmann（2007）对共同破碎的检验是基于具有独立误差的回归模型。因此，目前还没有长记忆条件下的协整检验，需要进一步研究长记忆条件下的协整与协整之间的关系;为了在实证应用中获得一致的建模策略，还需要深入理解伪长记忆现象，进而在多元背景下理解协整与协整之间的关系。因此，一方面，我们考虑哪些属性区分过程的结构性断裂和类似的自相关结构作为一个长记忆过程的过程与真正的长程依赖性。一个可能的性质可能是泛函中心极限定理的有效性。此外，结构突变可能产生双曲线衰减的自相关函数。但是它收敛到一个正的常数，并且不像在长记忆情况下那样为零。结果也将推广到多变量的情况。Leschinski & Sibbertsen（2017）的研究结果也表明，协破可能会导致虚假的分数协整。此外，本文还将运用所发展的统计方法对金融数据进行实证研究，进一步考察协破对投资组合选择的影响。此外，将评估对已实现相关性的预测质量。

Motivation of the second project phase is the work of Bertram, Kruse & Sibbertsen (2013) who find long-range dependencies as well as structural breaks in realized correlations of american stock returns. Furthermore, the breaks seem to happen at the same time points. This empirical regularity raises several research questions.Firstly, the long-range dependencies discovered in the data may be due to structural changes. Therefore, a multivariate algorithm is needed which tests for structural breaks and is robust against long memory.Secondly, the identical time points of the structural breaks may suggest a co-breaking relation between the time series. The test of Hendry & Massmann (2007) on co-breaking is based on a regression model with independent errors, though. Thus, there is no test for co-breaking under long memory at hand and such a test needs to be developed to gain further insight in the connection between co-breaking and long-range dependencies.For a consistent modelling strategy in empirical applications it is also necessary to have a deeper understanding about the phenomenon of spurious long memory and thus in the multivariate context about the connection between cointegration and co-breaking. Therefore, we consider on the one hand which properties distinguish processes with structural breaks and a similar autocorrelation structure as a long-memory process of processes with true long-range dependencies. One posiible property may be the validity of a functional central limit theorem. Furthermore may structural breaks create a hyperbolically decaying autocorrelation function. But it converges to a positive constant and does not vanish as it does in the long-memory case. The results will also be generalized to the multivariate case. The results of Leschinski & Sibbertsen (2017) also indicate that co-breaking may cause spurious fractional cointegration.Furthermore, the developed statistical methods will be applied in an empirical study to finance data to further investigate the consequences of co-breaking to the selection of portfolios. Also, the quality of forecasts for realized correlations will be evaluated.