In macroeconomic theory and economic policy, changes in the general price level or the rate of inflation plays an essential role. Hence, for example, one of the motives behind the adoption of Inflation Targeting policy (IT) by Ghana and the treaty espoused by the European Monetary Union, known as the Maastricht Treaty, was the convergence of inflation rates. On the other hand there is a controversy about which is the order of integration in the inflation rates, some authors arguing that this variable is stationary I(0) Whittle others saying it is nonstationary I(1). In this study we examine the CPI inflation rates of Ghana from a different perspective allowing for fractional degrees of differentiation. Thus, the methodology is based on long memory or long-range dependence processes, using fractional integration and employing techniques based on Whittle parametric and semiparametric methods and autoregressive fractionally integrated moving average (ARFIMA) models. Standard I(0)/I(1) methods were also employed. Our findings indicate that long memory exists in the CPI inflation rate of Ghana. After processing fractional differencing and determining the short memory components, the following two models, ARFIMA(3,0.427,1) and ARFIMA(2,0.499,1) were respectively specified to describe the pre and post introduction of IT policy in May 2007. Consequently, the CPI inflation rate of Ghana is fractionally integrated and mean reverting. Long memory in financial time series has important implications for the critical explanation of financial time series behaviour, as it could provide an opportunity to earn speculative profits in financial markets and cast disbelief on the correctness of the EMH. For instance, when price changes exhibit long memory or long-range dependence, asset pricing models based on the Efficient Market Hypothesis (EMH) may overestimate or underestimate investment risk. Furthermore, the presence of long memory in inflation rates can provide vital information about the likely impact of shocks (e.g. demand/supply) on the economy with respect to time. The results obtained in this study would be very useful in setting up monetary policies or consolidating previous policies such as IT in order to enhance economic growth. Moreover, estimation of long memory in inflation rates can serve as an evaluation tool to assess the performance of monetary policy under different dispensations. Lastly, the presence of long memory can assist in identifying inflationary pressures in the economy.