Using weekly data for stock and Forex market returns, a set of MS-GARCH models is estimated for a group of high-income (HI) countries and emerging market economies (EMEs) using algorithms proposed by Augustyniak (2014) and Ardia et al. (2018, 2019a,b), allowing for a variety of conditional variance and distribution specifications. The main results are: (i) the models selected using Ardia et al. (2018) have a better fit than those estimated by Augustyniak (2014), contain skewed distributions, and often require that the main coefficients be different in each regime; (ii) in Latam Forex markets, estimates of the heavy-tail parameter are smaller than in HI Forex and all stock markets; (iii) the persistence of the high-volatility regime is considerable and more evident in stock markets (especially in Latam EMEs); (iv) in (HI and Latam) stock markets, a single-regime GJR model (leverage effects) with skewed distributions is selected; but when using MS models, virtually no MS-GJR models are selected. However, this does not happen in Forex markets, where leverage effects are not found either in single-regime or MS-GARCH models.