Coherent Forecasting and Risk Analysis of Count Processes

• Applicant: Professor Dr. Christian Weiß
• Subject Area: Statistics and Econometrics
• Term: from 2018 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 394832307

Count time series appear in many circumstances of everyday life, and in particular in situations with an economic context. Count time series may show quite different characteristics, e.g., pronounced serial dependencies or marginal distributions with overdispersion or zero inflation. The forecasting of such time series is important for, e.g., the planning of demand, the assessment of economic development, or to prepare for a possible extreme situation (risk).To account for the integer character of counts when generating forecasts, coherent forecasting schemes lead to discrete predictions in a natural way, by computing the predictive distribution exactly and by then using, e.g., quantiles thereof. But since the calculation of the exact predictive distribution is not always obvious, practitioners often generate their count time series forecasts based on methods for real-valued time series, e.g., by using the Gaussian ARMA models as an approximation. Since a prediction generated in this way does generally not lead to non-negative and integer values, the resulting forecasts have to be truncated and rounded afterwards. The essential question is: How good does such kind of approximation of the true predictive distribution work, and how reliable are the forecasts generated in this way?The intended research project is centered around the coherent forecasting of count processes. The aim is to always compare a model-based and an approximate scheme for coherent forecasting. For the model-based scheme, a broad variety of models will be considered, besides INAR models with diverse marginal distributions (e.g., with overdispersion and zero inflation) and models for the case of a finite support also models allowing for trend and seasonality. For all these types of models, the quality of the resulting point and interval forecasts will be analyzed, also in the case of estimated model parameters.In the context of extreme forecasting quantiles, the more general question about a risk analysis based on count time series becomes relevant, which is the second main part of the intended research project. The aim is the prediction of a risk based on forecasting quantiles and on risk measures derived thereof, always based on conditional forecasting distributions (also under estimation uncertainty). It is intended to evaluate the goodness of the risk forecasts and to answer the question, which risk measure is best suited for the risk analysis of count time series.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Layth Alwan, Ph.D.
• Co-Investigators: Professor Dr. Gabriel Frahm; Professor Dr. Rainer Göb