This paper analyses the main statistical properties of the Emerging Market Bond Index (EMBI), namely long-range dependence or persistence, non-linearities, and structural breaks, in four Latin American countries (Argentina, Brazil, Mexico, Venezuela). For this purpose it uses a fractional integration framework and both parametric and semiparametric methods. The evidence based on the former is sensitive to the specification for the error terms, whilst the results from the latter are more conclusive in ruling out mean reversion. Further, non-linearities do not appear to be present. Both recursive and rolling window methods identify a number of breaks. Overall, the evidence of long-range dependence as well as breaks suggests that active policies might be necessary for achieving financial and economic stability in these countries.