Statistical inference of long-memory time series faces two challenges due to the special behavior of the sample sum 1)a non-standard fluctuation rate which is typically unknown 2)a family of non-Gaussian scaling limits arise and it is difficult to determine which one to use.We introduce a procedure which combines two strategies: self-normalization and resampling.Such a combination successfully bypasses the aforementioned challenges.To establish the validity of the procedure,a key result involving bounding the mixing coefficient between two finite blocks of a long-memory sequence is derived.In addition,the same procedure is also valid under short memory or heavy tails.It thus provides a unified inference procedure under various scenarios.