The effect of structural breaks on inference with stochastic processes subject to long memory

This DFG project is realized in corporation with the Institute of Statistics of Leibnitz University Hannover.

The project is motivated by Bertram, Kruse & Sibbertsen (2013), who find that correlations of American stock returns show long-term dependence as well as that there are structural breaks in the observed time series, possibly occurring at the same time points. This empirical regularity raises a number of questions. On the one hand, the long-term dependence structures themselves may possibly be due to structural breaks in the mean of the series. Therefore, it is necessary to derive an algorithm that can be used to test for structural breaks in multivariate time series and that is robust to long memory. On the other hand, the timing of the structural breaks suggests that a co-breaking relationship between the time series could exist. However, the co-breaking test proposed by Hendry & Massmann (2007) is based on a regression model with independent disturbances, and currently no co-breaking test is available for long-memory data structures. A second goal of the project is therefore to develop such a test in order to investigate the interaction between co-breaking and long-term dependence.

In order to have a coherent modelling strategy for empirical application, it is also necessary to gain an understanding of seemingly long memory and thus of the interplay between cointegration and co-breaking. A further objective of the project is therefore to investigate which properties distinguish structural break processes, which have autocorrelation structures similar to those with long memory, from processes with true long memory. One such property is the validity of functional central limit theorems. In addition, although the autocorrelation function of a structural break process can indeed show hyperbolic decay, it converges to a positive constant and not to zero, as in processes of true long memory. The findings are then generalised to the case of multivariate time series systems. The results of Leschinski & Sibbertsen (2017) suggest that co-breaking leads to an apparent fractional cointegration. 

A final goal of the project is to apply the newly derived statistical methods to financial market data in a detailed empirical study to investigate both the impact of co-breaking on portfolio selection and the accuracy of forecasts of realized correlations.