Fluctuation Analysis of Volatility in South African Stock Market Indices

Abstract The COVID-19 pandemic in 2020 had a significant impact on the global economy, leading to a sharp decline in stock index values. This study examines major stock market indices listed on the Johannesburg Stock Exchange from 2012 to 2024, analyzing their realized volatility time series and its distinctive characteristics before, during, and after the pandemic. We apply multifractal detrended fluctuation analysis ( Mf-DFA ) and the microstructure noise index ( MNI ) approach to evaluate the multifractality of the realised volatility of these South African stock indices. Results indicate that (log) volatility is anti-persistent or “rough”, both before and after the pandemic, with the Hurst parameter H ranging from 0.2 to 0.3. Furthermore, we observe that volatility is multifractal, characterised by a nonconstant generalised Hurst exponent h ( q ). The multifractality deviation indices for both shuffled time series and Iterated Amplitude Adjusted Fourier Transform (IAAFT) surrogates range between 0.7 and 1.6, suggesting that multifractality originates largely from temporal correlations in both small and large fluctuations. In addition, the variability indices are low, around 0.01 to 0.02, indicating that multifractality is primarily due to nonlinear correlations. An exception was noted in the realised volatility of the JSE Financials and Industrials Index during the pandemic, influenced further by economic uncertainty due to geopolitical tensions.