The eventual success of many AR and VR intelligent interactive systems relies on the ability to collect user motion data at large scale. Realistic simulation of human motion trajectories is a potential solution to this problem. Simulated user motion data can facilitate prototyping and speed up the design process. There are also potential benefits in augmenting training data for deep learning-based AR/VR applications to improve performance. However, the generation of realistic motion data is nontrivial. In this paper, we examine the specific challenge of simulating index finger movement data to inform mid-air gesture keyboard design. The mid-air gesture keyboard is deployed on an optical see-through display that allows the user to enter text by articulating word gesture patterns with their physical index finger in the vicinity of a visualized keyboard layout. We propose and compare four different approaches to simulating this type of motion data, including a Jerk-Minimization model, a Recurrent Neural Network (RNN)-based generative model, and a Generative Adversarial Network (GAN)-based model with two modes: style transfer and data alteration. We also introduce a procedure for validating the quality of the generated trajectories in terms of realism and diversity. The GAN-based model shows significant potential for generating synthetic motion trajectories to facilitate design and deep learning for advanced gesture keyboards deployed in AR and VR.