Analysis and Forecasting of Risk in Count Processes

Annika Homburg, Christian H. Weiß, Gabriel Frahm, Layth C. Alwan and Rainer Göb
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Annika Homburg: Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany
Christian H. Weiß: Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany
Gabriel Frahm: Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany
Layth C. Alwan: Sheldon B. Lubar School of Business, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA
Rainer Göb: Department of Statistics, Institute of Mathematics, University of Würzburg, 97070 Würzburg, Germany

JRFM, 2021, vol. 14, issue 4, 1-25

Abstract: 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.

Keywords: count time series; expected shortfall; expectiles; Gaussian approximation; mid quantiles; tail conditional expectation; value at risk (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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