Institute of Statistics

Workgroup "Time Series of functional data"

• Prof. Dr. Holger Dette
  
• Dr. Gauthier Dierickx
  
• Dr. Tim Kutta
  
• Lujia Bai
  

Description:

A key task in applied statistics is to analyse the development of a certain quantity in time. When discretely observed, such data are called a "time series". Typical examples come from econometrics (development of a price) or life sciences (growth of a being) among others, and already quite simple cases suggest that the analysis of such time series is much more involved than in the classical case of independent and identically distributed variables. Regarding independence, this is almost always the case, as the value or the increment of a certain time series is usually highly dependent on those in the recent past. To abstain from the identical distribution is less inevitable, as it is often reasonable to work with models that assume a homogeneuous ("stationary") behaviour in time. But there are also models incorporating times of slow or rapid growth or general (yearly, say) periodic oscillations of characteristic variables such as the mean or quantiles. To analyse these different kinds of periodicity is one focus of the group on time series. Besides, we develop tools for model validation, that is we check to which extent a certain model is adequate for a specific time series. This is done by defining reasonable measures of distance and constructing statistical tests based on appropriate empirical versions of those.