Time series analysis in reconstructed phase spaces

Time series analysis is a statistical analysis of sequences of data, where temporal correlations are to be characterized and interpreted. Depending on the hypothesis about the source of such correlations, different techniques can be employed. In this talk we focus on the reconstruction of vector valued auxillary spaces from the observed data, which serve as a state space for the dynamics of the data. We discuss the issue of state space reconstruction, of determnistic and stochastic modelling in these spaces, and of non-stationarity. The methods are illustrated by applications such as prediction of surface wind velocities and noise reduction for human voice.