This paper deals with the analysis of crude oil prices in the context of fractional integration and
using bull and bear phases over monthly periods between September, 1859 to July, 2015. We
examine both the log prices series as well as volatility, approximated by means of the absolute
and the squared returns. The results for the whole sample indicate that the log-prices are
nonstationary, with an order of integration close to 1 or even higher than 1, while the squared
and absolute returns show evidence of long memory behavior. Upon separating the sample
according to bull and bear periods, we observe an increase in the order of integration in both the
log-prices and the two measures of volatility. Our results have important policy implications.