Following Varneskov and Perron (2014), I apply the RLS-ARFIMA(0,d,0) and the RLS-ARFIMA (1,d,1) models to the daily stock and Forex market returns volatility of Argentina, Brazil, Chile, Mexico and Peru. It is a parametric state-space model with an estimation framework that combines long memory and level shifts by decomposing the underlying process into a simple mixture model and ARFIMA dynamics. The full sample parameters estimates show that level shifts are rare but they are present in all series. A genuine long-memory component is present in volatility of some countries and the results suggest that the remaining short-memory component is nearly uncorrelated once the level shifts are accounted for. I compare the results with four RLS models as in Xu and Perron (2014) and applied in Rodríguez (2016) for same Latin-American series. An out-of-sample forecasting comparison is also perform...