Empirical research indicates that the volatility of stock return time series have long memory. However, it has been demonstrated that short memory processes contaminated with random level shifts can often be confused as being long memory. Often this feature is referred to as spurious long memory. This paper represents an empirical study of the random level shift (RLS) model using the approach of Lu and Perron (2010) and Li and Perron (2013) for the volatility of daily stocks returns data for five Latin American countries. The RLS model consists of the sum of a short term memory component and a level shift component, where the level shift component is governed by a Bernoulli process with a shift probability (alpha). The estimation results suggest that the level shifts in the volatility of daily stocks returns data are infrequent but once they are taken into account, the long memory characteristic and the GARCH e¤ects disappear. An out-of-sample forecasting exercise is also provided.