Quasi-likelihood deconvolution of non-gaussian non-invertible moving average model

In reflection seismology the reflectivity sequence is of primary interest and must be estimated. Estimation of the reflectivity sequence is based on deconvolution of seismic trace data. Modelling the seismic trace as the non-Gaussian moving average time series, we propose a deconvolution method based on the modified L₂ estimation, which is consistent estimation of moving average models with heavy tailed error distribution. The asymptotical equivalence is established between the proposed method and the deconvolution using O²₁. Simulation studies are presented to validate the equivalency. Furthermore, based on this equivalence the consistency problem of the O²₁ deconvolution has been discussed.