We consider the wavelet-based approximate maximum likelihood estimation problem of the memory parameter for long-memory process with noise models, where the long-memory process is assumed to be stationary or non-stationary case, and the noise is assumed to be white noise process and independent of the long-memory process. Whereas Tanaka(2004) use the white-noise (WN) approximation to investigate this problem, using the AR(1) approximation to the wavelet coefficients of long-memory process at each scale, we fit the ARMA(1,1) process to the wavelet coefficients of long-memory process with noise model at each scale. We compare the performance of the two approximations by some simulations. |