Cooperative communications is a core research area in wireless vehicular networks (WVNs), thanks to its capability to mitigate fading and improve spectral efficiency. In a cooperative scenario, the performance of the system is improved by selecting the best relay for data transmission among a group of available relays. However, due to the mobility of WVNs, the best relay is often selected in practice based on outdated channel state information (CSI), which in turn affects the overall system performance. Therefore, there is a need for a robust relay selection scheme (RSS) that improves the overall achievable performance of an outdated CSI. Motivated by this and considering the advantageous features of autoregressive moving average (ARMA), in the present work we model a cooperative vehicular communication scenario with relay selection as a Markov decision process (MDP) and propose two deep Q-networks (DQNs), namely DQN-RSS and DQN-RSS-ARMA. In the proposed framework, two deep reinforcement learning (RL)-based RSS are trained based on the intercept probability, aiming to select the optimal vehicular relay from a set of multiple relays. We then compare the proposed RSS with the conventional methods and evaluate the performance of the network from the security point of view. Simulation results show that DQN-RSS and DQN-RSS-ARMA perform better than conventional approaches, and they reduce intercept probability by approximately 15\% and 30\%, respectively, compared to the ARMA approach.