Efficient Detection and Estimation of Multiple Structural Breaks in Cointegrated Systems

• Applicant: Dr. Karsten Schweikert
• Subject Area: Statistics and Econometrics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 449607135

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.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Robert C. Jung