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

• Applicants: Professor Dr. Michael Massmann; Professor Dr. Philipp Sibbertsen
• Subject Area: Statistics and Econometrics
• Term: from 2014 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258395632

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.

• DFG Programme: Research Grants