Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related Field

Some Econometric Evidence on the Effectiveness of Active Labour Market Programmes in East Germany

In this paper we summarise our previous results on the effectiveness of different kinds of labour market training programmes as well as employment programmes in East Germany after unification. All the studies use the microeconometric evaluation approach and are based on different types of matching estimators. We find some positive earnings effect for on-the-job training and also some positive employment effects for employment programmes. No such effects appear for public sector sponsored (off-the-job) training programmes. Generally, the scope of such analysis is very much hampered by the insufficient quality and quantity of the data available for East Germany. Although in particular the results for public sector sponsored training programmes raise serious doubts about the effectiveness of these programmes, any definite policy conclusion from this and other studies about active labour market policy in East Germany would probably be premature.http://deepblue.lib.umich.edu/bitstream/2027.42/39702/3/wp318.pd

Locally Stationary Functional Time Series

The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be able to weaken this assumption. This paper introduces a framework that will enable meaningful statistical inference of functional data of which the dynamics change over time. We put forward the concept of local stationarity in the functional setting and establish a class of processes that have a functional time-varying spectral representation. Subsequently, we derive conditions that allow for fundamental results from nonstationary multivariate time series to carry over to the function space. In particular, time-varying functional ARMA processes are investigated and shown to be functional locally stationary according to the proposed definition. As a side-result, we establish a Cram\'er representation for an important class of weakly stationary functional processes. Important in our context is the notion of a time-varying spectral density operator of which the properties are studied and uniqueness is derived. Finally, we provide a consistent nonparametric estimator of this operator and show it is asymptotically Gaussian using a weaker tightness criterion than what is usually deemed necessary