Modeling Latin-American Stock and Forex Markets Volatility: Empirical Application of a Model with Random Level Shifts and Genuine Long Memory [Modelando la volatilidad de los mercados bursátiles y cambiarios en América Latina: Aplicación empírica de un modelo de cambios de nivel aleatorios y larga memoria genuina]

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 performed using the approach of Hansen et al. (2011). The RLS-ARFIMA models presents better performance for some horizons while the other four RLS models are better for other horizons. In none horizon of forecasting, simple ARFIMA models are selected or belong to the 10% of the MCS of Hansen et al. (2011).