Identification of multivariate dynamic systems

This project is concerned with data driven modeling of multivariate times series with a special emphasis on dimension reduction. In general terms dimension reduction is concerned with systematically finding lower dimensional structures which give a good explanation of high dimensional data sets. We consider different model classes, namely stable and unit roots linear state-space systems, static and dynamic linear factor models and multivariate GARCH models. Questions of parametrization, estimation and model selection are considered. For all these model classes dimension reduction is an issue, in particular for high dimensional data sets. There is a broad range of applications for the models and methods considered. Our emphasis will be on applications to financial data. In particular, we consider the following four problems: Parametrizations for multivariate linear state-space systems and their effects on numerical properties of identification algorithms. A further continuation of the investigation of data driven local coordinates for state-space systems is intended. A special emphasis will be on the so-called slsDDLC procedures which allow for a dimension reduction of the parameter spaces by performing a concentration step for the likelihood function. Parametrization and estimation for unit root systems with an emphasis on (polynomial) cointegration. The main aim of cointegration analysis is to decompose the observed variables into a stationary part and a part generated by a few common trends, where the economically relevant information lies in the cointegrating relations. Recently, parametrizations for general unit roots processes in the state-space framework have been introduced, which highlight the (polynomial) cointegration properties. The usage of these parametrizations for estimation will be examined. The topics considered here are closely related to the problem stated above. In particular, we plan to extend the ideas of data driven local coordinates to the unit roots case. Dynamic factor models for forecasting financial time series. As is well known, factor models are a classical tool for dimension reduction. The idea here is to explain the main features of the observed variables by a few factor variables, which then allows for lower dimensional parametrizations. Recently factor models have gained great importance for modeling of financial time series. Whereas the classical use of factor models is data analysis, the emphasis here will be on forecasting, which poses a number of methodological questions. In particular, we want to include exogenous variables for forecasting the factors. Multivariate volatility models with a special emphasis on finding appropriate lower dimensional model classes. As is well known, even for a moderate number of variables the dimension of the parameter space for fully parametrized GARCH models is prohibitive. To overcome these problems restricted model classes like the BEKK classes and factor GARCH models have been introduced. Our intention is to clarify parametrization issues and to develop tools for deciding which model classes are appropriate in a specific context.

This project is concerned with data driven modeling of multivariate times series with a special emphasis on dimension reduction. In general terms dimension reduction is concerned with systematically finding lower dimensional structures which give a good explanation of high dimensional data sets. We consider different model classes, namely stable and unit roots linear state-space systems, static and dynamic linear factor models and multivariate GARCH models. Questions of parametrization, estimation and model selection are considered. For all these model classes dimension reduction is an issue, in particular for high dimensional data sets. There is a broad range of applications for the models and methods considered. Our emphasis will be on applications to financial data. In particular, we consider the following four problems: Parametrizations for multivariate linear state-space systems and their effects on numerical properties of identification algorithms. A further continuation of the investigation of data driven local coordinates for state-space systems is intended. A special emphasis will be on the so-called slsDDLC procedures which allow for a dimension reduction of the parameter spaces by performing a concentration step for the likelihood function. Parametrization and estimation for unit root systems with an emphasis on (polynomial) cointegration. The main aim of cointegration analysis is to decompose the observed variables into a stationary part and a part generated by a few common trends, where the economically relevant information lies in the cointegrating relations. Recently, parametrizations for general unit roots processes in the state-space framework have been introduced, which highlight the (polynomial) cointegration properties. The usage of these parametrizations for estimation will be examined. The topics considered here are closely related to the problem stated above. In particular, we plan to extend the ideas of data driven local coordinates to the unit roots case. Dynamic factor models for forecasting financial time series. As is well known, factor models are a classical tool for dimension reduction. The idea here is to explain the main features of the observed variables by a few factor variables, which then allows for lower dimensional parametrizations. Recently factor models have gained great importance for modeling of financial time series. Whereas the classical use of factor models is data analysis, the emphasis here will be on forecasting, which poses a number of methodological questions. In particular, we want to include exogenous variables for forecasting the factors. Multivariate volatility models with a special emphasis on finding appropriate lower dimensional model classes. As is well known, even for a moderate number of variables the dimension of the parameter space for fully parametrized GARCH models is prohibitive. To overcome these problems restricted model classes like the BEKK classes and factor GARCH models have been introduced. Our intention is to clarify parametrization issues and to develop tools for deciding which model classes are appropriate in a specific context.