The Wavelet-based Estimation for Long Memory Signal Plus Noise Models

We propose new wavelet-based procedure to estimate the memory parameter of an unobserved process from an observed process affected by noise in order to improve the performance of the estimator by taking into account the dependency of the wavelet coefficients of long memory processes. In our procedure, using the AR (1) approximation for the wavelet transformed long memory processes which is introduced by Craigmile, Guttorp and Percival (2005), we apply the ARMA (1, 1) approximation to the wavelet coefficients of the observed process at each level. We also compare this procedure to the usual wavelet-based procedure by numerical simulations.