TY  - JOUR
A1  - Homburg, Annika
A1  - Weiß, Christian H.
A1  - Frahm, Gabriel
A1  - Alwan, Layth C.
A1  - Göb, Rainer
T1  - Analysis and forecasting of risk in count processes
JF  - Journal of Risk and Financial Management
N2  - Risk measures are commonly used to prepare for a prospective occurrence of an adverse event. If we are concerned with discrete risk phenomena such as counts of natural disasters, counts of infections by a serious disease, or counts of certain economic events, then the required risk forecasts are to be computed for an underlying count process. In practice, however, the discrete nature of count data is sometimes ignored and risk forecasts are calculated based on Gaussian time series models. But even if methods from count time series analysis are used in an adequate manner, the performance of risk forecasting is affected by estimation uncertainty as well as certain discreteness phenomena. To get a thorough overview of the aforementioned issues in risk forecasting of count processes, a comprehensive simulation study was done considering a broad variety of risk measures and count time series models. It becomes clear that Gaussian approximate risk forecasts substantially distort risk assessment and, thus, should be avoided. In order to account for the apparent estimation uncertainty in risk forecasting, we use bootstrap approaches for count time series. The relevance and the application of the proposed approaches are illustrated by real data examples about counts of storm surges and counts of financial transactions.
KW  - count time series
KW  - expected shortfall
KW  - expectiles
KW  - Gaussian approximation
KW  - mid quantiles
KW  - tail conditional expectation
KW  - value at risk
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-236692
SN  - 1911-8074
VL  - 14
IS  - 4
ER  - 
TY  - JOUR
A1  - Homburg, Annika
A1  - Weiß, Christian H.
A1  - Alwan, Layth C.
A1  - Frahm, Gabriel
A1  - Göb, Rainer
T1  - Evaluating approximate point forecasting of count processes
JF  - Econometrics
N2  - In forecasting count processes, practitioners often ignore the discreteness of counts and compute forecasts based on Gaussian approximations instead. For both central and non-central point forecasts, and for various types of count processes, the performance of such approximate point forecasts is analyzed. The considered data-generating processes include different autoregressive schemes with varying model orders, count models with overdispersion or zero inflation, counts with a bounded range, and counts exhibiting trend or seasonality. We conclude that Gaussian forecast approximations should be avoided.
KW  - count time series
KW  - estimation error
KW  - Gaussian approximation
KW  - predictive performance
KW  - quantile forecasts
KW  - Value at Risk
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-196929
SN  - 2225-1146
VL  - 7
IS  - 3
ER  - 
TY  - JOUR
A1  - Homburg, Annika
A1  - Weiß, Christian H.
A1  - Alwan, Layth C.
A1  - Frahm, Gabriel
A1  - Göb, Rainer
T1  - A performance analysis of prediction intervals for count time series
JF  - Journal of Forecasting
N2  - One of the major motivations for the analysis and modeling of time series data is the forecasting of future outcomes. The use of interval forecasts instead of point forecasts allows us to incorporate the apparent forecast uncertainty. When forecasting count time series, one also has to account for the discreteness of the range, which is done by using coherent prediction intervals (PIs) relying on a count model. We provide a comprehensive performance analysis of coherent PIs for diverse types of count processes. We also compare them to approximate PIs that are computed based on a Gaussian approximation. Our analyses rely on an extensive simulation study. It turns out that the Gaussian approximations do considerably worse than the coherent PIs. Furthermore, special characteristics such as overdispersion, zero inflation, or trend clearly affect the PIs' performance. We conclude by presenting two empirical applications of PIs for count time series: the demand for blood bags in a hospital and the number of company liquidations in Germany.
KW  - coherent forecasting
KW  - count time series
KW  - estimation error
KW  - Gaussian approximation
KW  - prediction interval
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-217906
VL  - 40
IS  - 4
SP  - 603
EP  - 609
ER  -