In this paper, the improvement of the cascaded prediction method was presented. Three types of main predictor block with different levels of complexity were compared, including two complex prediction methods with backward adaptation, i.e., extension Active Level Classification Model (ALCM+) and extended Ordinary Least Square (OLS+). Our own approach to implementation of the effective context-dependent constant component removal block is also presented. Additionally, the improved adaptive arithmetic coder with short, medium and long-term adaptation was presented, and the experiment was carried out comparing the results with other known lossless audio coders against which our method obtained the best efficiency.