In this paper, we analyze the performance of five estimation methods for the long memory parameter d. The goal of our paper is to construct a wavelet estimate for the fractional differencing parameter in nonstationary long memory processes which dominate the well known estimate of Shimotsu and Phillips (2005). The simulation results show that the wavelet estimation method of Lee (2005) with several tapering techniques performs better under most cases in nonstationary long memory. The comparison is based on the empirical root mean squared error of each estimate.