Institute of Mathematical Statistics and Actuarial Science

Forecasting theory and applications

Group leader: Prof. Dr. Johanna Ziegel

Forecasts for unknown future events are ubiquitous. Since decisions of great impact are based on such forecasts, objective forecast evaluation and comparison are of utmost importance. We are conducting research on decision theoretically sound methods for forecast evaluation and comparison. This often also leads to new methods for the modeling of random phenomena and for data analysis. Recent progress in this direction concerns distributional regression under order constraints. Furthermore, there are connections to other areas such as risk measures in mathematical finance. We consider applications in areas such as meteorology, finance and medicine.

Collaborations

The group is involved in several national and international collaborations on a variety of topics. In particular, there is close exchange with the Computational Statistics group at the Heidelberg Institute of Theoretical Studies (HITS) in Germany headed by Prof. Tilmann Gneiting (HITS and KIT). The group is a member of the Oeschger Centre for Climate Change Research (OCCR) and there is collaboration with other groups of the OCCR, namely with the groups of Professor Olivia Romppainen-Martius and Professor Bettina Schläfli. Together with Professor David Ginsbourger, there is ongoing research with the Federal Office for Meteorology and Climatology (MeteoSwiss), with focus on statistical postprocessing and the evaluation of warnings.

Selected publications

A. Henzi, J. F. Ziegel. Valid sequential inference on probability forecast performance. Biometrika, to appear, 2021+. [arXiv:2103.08402]
A. Henzi, J. F. Ziegel, T. Gneiting. Isotonic distributional regression. Journal of the Royal Statistical Society: Series B, 83:963–993, 2021. [DOI:10.1111/rssb.12450]
A. Henzi, G.-R. Kleger, J. F. Ziegel. Distributional (single) index models. Journal of the American Statistical Association, to appear, 2021+. [arXiv:2006.09219]
I. Steinwart, J. F. Ziegel. Strictly proper kernel scores and characteristic kernels on compact spaces. Applied and Computational Harmonic Analysis, 51:510–542, 2021. [DOI:10.1016/j.acha.2019.11.005]
T. Fissler, J. F. Ziegel. Higher order elicitability and Osband’s principle. Annals of Statistics, 44:1680–1707, 2016. [DOI:10.1214/16-AOS1439]
J. F. Ziegel. Coherence and elicitability. Mathematical Finance, 26:901–918, 2016. [DOI:10.1111/mafi.12080]