Forecasting the motion of the leading vehicle is a critical task for connected autonomous vehicles as it provides an efficient way to model the leading-following vehicle behavior and analyze the interactions. In this study, a personalized time-series modeling approach for leading vehicle trajectory prediction considering different driving styles is proposed. The method enables a precise, personalized trajectory prediction for leading vehicles with limited inter-vehicle communication signals, such as vehicle speed, acceleration, space headway, and time headway of the front vehicles. Based on the learning nature of human beings that a human always tries to solve problems based on grouping and similar experience, three different driving styles are first recognized based on an unsupervised clustering with a Gaussian Mixture Model (GMM). The GMM generates a specific driving style for each vehicle based on the speed, acceleration, jerk, time, and space headway features of the leading vehicle. Then, a personalized joint time-series modeling (JTSM) method based on the Long Short-Term Memory (LSTM) Recurrent Neural Network model (RNN) is proposed to predict the trajectory of the front vehicle. The JTSM contains a joint LSTM layer and different fully-connected regression layers for different driving styles. The proposed method is tested with the Next Generation Simulation (NGSIM) data on US101, and I-80. The JTSM is tested for making predictions one second ahead. Results indicate that the proposed personalized JTSM approach shows a significant advantage over the other algorithms.