Analysis and forecasting of risk in count processes

Homburg, Annika; Weiß, Christian H.; Frahm, Gabriel; Alwan, Layth C.; Göb, Rainer

doi:10.3390/jrfm14040182

Analysis and forecasting of risk in count processes

Publication date

2021-04-16

Document type

Forschungsartikel

Author

Homburg, Annika

Weiß, Christian H.

Frahm, Gabriel

Alwan, Layth C.

Göb, Rainer

Organisational unit

Quantitative Methoden der Wirtschaftswissenschaften

Angewandte Stochastik und Risikomanagement

DOI

10.3390/jrfm14040182

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/22436

Scopus ID

2-s2.0-85108244315

Publisher

MDPI AG

Series or journal

Journal of Risk and Financial Management

ISSN

1911-8066

Periodical volume

14

Periodical issue

4

Article ID

182

Part of the university bibliography

✅

Language

English

Keyword

count time series

expected shortfall

expectiles

Gaussian approximation

mid quantiles

tail conditional expectation

value at risk

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.

Description

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Version

Published version

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