Optimal threshold determination based on the mean excess plot

Abstract

Choosing a suitable threshold has been an issue in practice. Based on the mean excess plot (MEP), the eyeball inspection approach (EIA) is mainly used to determine the threshold. This involves fitting the threshold at the point the plot becomes approximately linear solely using one’s sense of judgement in such a way that Generalized Pareto model is valid. This is a rather subjective choice. In this paper, we propose an alternative way of selecting the threshold where, instead of choosing individual thresholds in isolation and testing their fit, we make use of the bootstrap aggregate of these individual thresholds which are formulated in terms of quantiles.The method incorporates the visual technique and is aimed at reducing the subjectivity associated with solely using the EIA. The new approach is implemented using simulated datasets drawn from three different distributions. An application to the NSE All share Nigerian stock index is presented. The performance of the proposed model and the EIA are judged based on standard error, Negative log likelihood, the Akaike Information Criteria and the Bayesian Information Criteria. The results show that the new technique gives similar estimates as the EIA and in some cases it performs better. In comparison to other existing methods, the proposed model performs well.

Keywords:

• Mean excess plot
• Peaks-over-threshold model
• Order statistics
• Generalized Pareto distribution
• quantile modeling
• bootstrap aggregation

Additional information

Funding

Pan African University Institute for Basic Sciences, Technology and Innovation, Kenya.