Partial compact quantum groups

Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multiplier bialgebra and weak multiplier Hopf algebra (resp. due to B{\"o}hm--G\'{o}mez-Torrecillas--L\'{o}pez-Centella and Van Daele-Wang), we generalize Hayashi's definition to allow for an infinite set of objects, and call the resulting objects partial compact quantum groups. We prove a Tannaka-Kre$\breve{\textrm{\i}}$n-Woronowicz reconstruction result for such partial compact quantum groups using the notion of a partial fusion C$^*$-category. As examples, we consider the dynamical quantum $SU(2)$-groups from the point of view of partial compact quantum groups.Comment: 56 page

How Informative are the Subjective Density Forecasts of Macroeconomists?

In this paper, we propose a framework to evaluate the information content of subjective expert density forecasts using micro data from the ECB’s Survey of Professional Forecasters (SPF). A key aspect of our analysis is the use of scoring functions which evaluate the entire predictive densities, including an evaluation of the impact of density features such as their location, spread, skew and tail risk on density forecast performance. Overall, we find considerable heterogeneity in the performance of the surveyed densities at the individual level. Relative to a set of crude benchmark alternatives, this performance is somewhat better for GDP growth than for inflation, although in the former case it diminishes substantially with the forecast horizon. In addition, relative to the proposed benchmarks, we report evidence of some improvement in the performance of expert densities during the recent period of macroeconomic volatility. However, our analysis also reveals clear evidence of overconfidence or neglected risks in the expert probability assessments, as reflected also in frequent occurrences of events which are assigned a zero probability. Moreover, higher moment features of the expert densities, such as their skew or the degree of probability mass in their tails, are shown not to contribute significantly to improvements in individual density forecast performance.density forecasts, forecast evaluation, real-time data, Survey of Professional Forecasters