Motion prediction for the leading vehicle is a critical task for connected autonomous vehicles. It provides a method to model the leading-following vehicle behavior and analysis their interactions. In this study, a joint time-series modeling approach for leading vehicle trajectory prediction considering different driving styles is proposed. The proposed method enables a precise and personalized trajectory prediction for the leading vehicle based on limited inter-vehicle communication signals, such as the vehicle speed and acceleration of the front vehicles. Three different driving styles are first recognized based on an unsupervised clustering algorithm, namely, 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. The feature importance of driving style recognition is also evaluated based on the Maximal Information Coefficient (MIC) algorithm. 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 front vehicle trajectories. The JTSM contains a common 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 the US101, and I-80 highway dataset. The JTSM is tested for making predictions one to five seconds ahead. Results indicate that the proposed personalized JTSM approach shows a significant advantage over the baseline algorithms.