Modeling and forecasting multivariate time series

This proposal is concerned with modeling and forecasting of high dimensional time series, with a focus on dimension reduction. The following three areas are considered: Generalized linear dynamic factor models. Here the emphasis is laid on model specification (e.g. on estimation of the factor dimension), on selection of variables suited for factor analysis and on detection of zero patterns in the factor loading matrix (indicating factors which load only on part of the observations) Input selection and reduced rank linear dynamic models (in cases where the classification of the observations into inputs and outputs is known a priori) Graphical time series analysis, where causal relations between the variables are analysed The intended development and evaluation of the methods and procedures is motivated by the needs of applications. We plan not only to test these methods with real data, but also to apply them to obtain actual forecasting models. The main area of application will be finance data, but we also plan to use sales or macroeconomic data.

The project consisted of two parts. In the first part the structure of multivariate time series has been investigated. A special focus here was on the detection of causal relations between time series components. A special methodology has been developed to analyse such causal relations for high dimensional time series in order to overcome numerical difficulties. The corresponding methods have been applied to the analysis of EEG data in order to localize the focus of epileptic seizures. The idea thereby is that the focus is the starting point of an epileptic seizure which in heavy cases might be removed by surgical intervention.In the second part of the project multivariate time series, where the univariate components are sampled at different frequencies, have been considered. Such data are called mixed frequency data. This is of particular importance for instance in macroeconomic applications where e. g. finance data typically are sampled at higher frequencies, e. g. daily, compared to real data such as GDP, which typically is available quarterly. Here results allowing to retrieve the parameters of the underlying high frequency system from mixed frequency data have been derived.