The recent accelerated growth in the computing power has generated popularization of experimentation with dynamic computer models in various physical and engineering applications. Despite the extensive statistical research in computer experiments, most of the focus had been on the theoretical and algorithmic innovations for the design and analysis of computer models with scalar responses. In this article, we propose a computationally efficient statistical emulator for a large-scale dynamic computer simulator (i.e., simulator which gives time series outputs). The main idea is to first find a good local neighborhood for every input location, and then emulate the simulator output via a singular value decomposition (SVD) based Gaussian process (GP) model. We develop a new design criterion for sequentially finding this local neighborhood set of training points. Several test functions and a real-life application have been used to demonstrate the performance of the proposed approach over a naive method of choosing local neighborhood set using the Euclidean distance among design points. The supplementary material, which contains proof of the theoretical results, detailed algorithms, additional simulation results, and R codes, are available online.