Existing depth sensing techniques have many shortcomings in terms of resolution, completeness, and accuracy. The performance of 3-D broadcasting systems is therefore limited by the challenges of capturing high-resolution depth data. In this paper, we present a novel framework for obtaining high-quality depth images and multi-view depth videos from simple acquisition systems. We first propose a single depth image recovery algorithm based on auto-regressive (AR) correlations. A fixed-point iteration algorithm under the global AR modeling is derived to efficiently solve the large-scale quadratic programming. Each iteration is equivalent to a nonlocal filtering process with a residue feedback. Then, we extend our framework to an AR-based multi-view depth video recovery framework, where each depth map is recovered from low-quality measurements with the help of the corresponding color image, depth maps from neighboring views, and depth maps of temporally adjacent frames. AR coefficients on nonlocal spatiotemporal neighborhoods in the algorithm are designed to improve the recovery performance. We further discuss the connections between our model and other methods like graph-based tools, and demonstrate that our algorithms enjoy the advantages of both global and local methods. Experimental results on both the Middleburry datasets and other captured datasets finally show that our method is able to improve the performances of depth images and multi-view depth videos recovery compared with state-of-the-art approaches.