A0642
Title: Simultaneous confidence bands for the PIT histogram
Authors: Matei Demetrescu - TU Dortmund University (Germany) [presenting]
Felix Kiessner - CAU Kiel (Germany)
Malte Knueppel - Bundesbank (Germany)
Abstract: The PIT histogram is a popular tool to check for uniformity of the PITs. The PITs are simply grouped into equally-sized bins, and if the resulting histogram does not appear to be flat, this suggests that the density forecasts lack calibration, i.e. that systematic errors occur. However, sometimes it is not obvious whether a histogram is sufficiently flat because small sample sizes and large numbers of bins might cause strong variations of the bin heights even under correct calibration. Well-founded decisions about whether forecasts are calibrated or not are possible using calibration tests. Yet, these tests might convey less information than visual inspections, because the latter may indicate the type of systematic error occurring. A simple method is proposed to construct simultaneous confidence bands for the PIT histogram. Simultaneous confidence bands facilitate a more informed decision about calibration than simple visual inspections. A bootstrap implementation is provided. The proposal is evaluated and compared to other approaches by means of Monte Carlo simulations, and it is applied to density forecasts derived from the survey of professional forecasters (SPF) of the Philadelphia Fed.
