Stationarity has always played an important role in the theoretical treatment of time series. However many series show a nonstationary behavior. In many cases, simple techniques such as differentiation is not enough. In this context, and considering the most frequent assumption of instability in the stochastic characteristics of financial returns as well as the consequences of assume stationarity when this feature is not reasonable, we use the methodology proposed by Picard (1985) (37), extended by Kluppelberg and Mikosch (1996) (23) and later by Starica and Granger (2005) (41), whose goal is to identify stationary periods in globally non-stationary series, and locally approximate them by stationary models. Aiming to broaden the understanding of the usefulness of the statistical methodology used, we made a simulation study involving structural or point changes in the generating process, and evaluating the performance of the methodology to detect these changes. This method of identifying homogeneous periods was applied in the context of Brazilian hedge funds, financial instruments where traditionally we see significant autocorrelation, even for long-term lags, feature explained in the literature as a result of illiquidity, as in Getmansky et al (2003) (14). Motivated by empirical evidence involving the influence of changes in non-conditional second moment of financial time series behavior of the function of serial correlation, discussed in Mikosch and Starica (2004) (32), we apply the methodology aiming identifying stationary periods in the hedge funds volatility series that had global non-stationarity.