The study looked into the stochastic properties of CPI-inflation rate for Nigeria from 1995Q1 to 2016Q4. The study employed an autoregressive fractionally integrated moving average and a general autoregressive conditional heteroskedasticity (ARFIMA-GARCH) methodology as well as ADF/KPSS to investigate the long-memory properties of CPI-Inflation for Nigeria. The study found that CPI-inflation in Nigeria is shock dissipating at a geometric rate (fast mean reverting ability). The ARFIMA-GARCH process showed that CPI inflation in Nigeria is a heteroskedastic fractionally integrated process with quick mean reverting ability. The study therefore concludes that shocks to CPI-inflation in Nigeria such as sudden hikes in prices of energy products will not cause a permanent change in general price level but will eventually return to its mean state, and therefore having an implication for the Inflation-Unemployment tradeoff of the Philips curve.