We present a no-reference (NR) quality assessment algorithm for assessing the perceptual quality of natural stereoscopic 3D (S3D) videos. This work is inspired by our finding that the joint statistics of the subband coefficients of motion (optical flow or motion vector magnitude) and depth (disparity map) of natural S3D videos possess a unique signature. Specifically, we empirically show that the joint statistics of the motion and depth subband coefficients of S3D video frames can be modeled accurately using a Bivariate Generalized Gaussian Distribution (BGGD). We then demonstrate that the parameters of the BGGD model possess the ability to discern quality variations in S3D videos. Therefore, the BGGD model parameters are employed as motion and depth quality features. In addition to these features, we rely on a frame-level spatial quality feature that is computed using a robust off-the-shelf NR image quality assessment (IQA) algorithm. These frame-level motion, depth and spatial features are consolidated and used with the corresponding S3D video's difference mean opinion score (DMOS) labels for supervised learning using support vector regression (SVR). The overall quality of an S3D video is computed by averaging the frame-level quality predictions of the constituent video frames. The proposed algorithm, dubbed Video QUality Evaluation using MOtion and DEpth Statistics (VQUEMODES) is shown to outperform the state-of-the-art methods when evaluated over the IRCCYN and LFOVIA S3D subjective quality assessment databases.