31, July 2025
Comparative analysis of Block Maxima method and Peak over Threshold method using Value at Risk forecasts of the South African Industrial Index
Author(s): Owen Jakata , Peter Chimwanda
Authors Affiliations:
1 Lecturer, Department of Human Resources Management, Faculty of Commerce, Bindura University of Science Education, Bindura, Zimbabwe
2 Lecturer, Department of Mathematics and Statistics, School of Natural Sciences and Mathematics, Chinhoyi University of Technology, Chinhoyi, Zimbabwe.
DOIs:10.2015/IJIRMF/202507047 | Paper ID: IJIRMF202507047Abstract
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Abstract: This study makes a comparative analysis of the Extreme Value Theory (EVT) methods using the monthly South African Industrial Index (J520) returns. The purpose is to investigate the comparative performance of the Block Maxima (BM) and Peak over Threshold (PoT) methods in the estimation of Value at Risk (VaR) for the period 1995 to 2018. The monthly return distribution is fitted to the Generalised Extreme Value Distribution (GEVD) and Generalised Pareto Distribution (GPD) using the maxima/minima extracted from the BM and PoT methods respectively. Parameters are estimated using the Maximum Likelihood Method (MLE) method. The parameter estimations show that the PoT method is the preferable model as it has a superior goodness of fit performance. The findings reveal that the VaR forecasts of the BM method are less than the PoT method. The results also reveal that for both methods the probability of losses is less than the probability of gains. Backtesting was carried out using the Kupiec test which validates that the PoT method is more preferable than the BM method. The contribution of this study is that it supports the evidence that the PoT method VaR forecasts are more reliable and satisfactory than the BM method VaR forecasts.
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Key Words:Â Back-testing; Block Maxima method; Extreme value theory; Generalized Extreme Value Distribution; Generalized Pareto Distribution; Kupiec Test; monthly South African Industrial Index (J520) returns; Peaks over Threshold method; Value at Risk.Â
Owen Jakata , Peter Chimwanda (2025); Comparative analysis of Block Maxima method and Peak over Threshold method using Value at Risk forecasts of the South African Industrial Index, International Journal for Innovative Research in Multidisciplinary Field, ISSN(O): 2455-0620, Vol-11, Issue-7, Pp.306-320.     Available on –  https://www.ijirmf.com/