AbstractsMathematics

This project aims to investigate developments of analysis methods for time series panel data proposed by Ranganathan et al.[94]. Model selection is used as a tool for data exploration. We obtain a more stable and consistent model selection by combining stability selection [82] on the adaptive LASSO [125] with some time series bootstrapping methods [88]. The resulting method is also computationally less heavy, allowing it to handle higher dimensional and higher order models. Further, a method for validating an estimated dynamic against local polynomial gradient estimates in the data is proposed. The introduced techniques are motivated in terms of related prior research. After this, a simulation study shows that the bootstrapped  stability selection is able to identify models for some non-linear diffusion processes. Finally, the model selection method is applied to real world data previously investigated by Ranganathan et al, giving results that do not match theirs. Implications and possible extensions are discussed. All the implemented procedures are available in packages for the R programming languages, such that one could easily continue investigating either of the introduced methods.