Persistence of Climate Risk in South Africa: Evidence from Rolling Local Whittle Estimation

We examine the persistence of climate-risk indicators in South Africa at the national, provincial, and municipal levels using the local Whittle estimator. Using the AgERA5 monthly indicators produced by the Actuarial Society of South Africa for the period January 1981 to May 2026, we estimate the fractional integration parameter over the full sample and re-estimate it within rolling ten-year and five-year windows. Full-sample estimates indicate that aggregate drought risk exhibits non-stationary, mean-reverting long memory, lying close to the unit-root boundary at the national level. In contrast, composite risk, extreme temperatures, and extreme precipitation exhibit shorter memory. Persistence, however, is not constant over time. At the national level, the memory parameters of the composite index and extreme maximum temperature rise almost monotonically over the sample, whereas those of extreme minimum temperature drift downward. At the provincial and municipal levels evidence reveals substantial heterogeneity that broadly aligns with the country's climatic zones. Our results are robust to the use of the alternative CHIRPS dataset.