Causal discovery in the form of a directed acyclic graph (DAG) for time series data has been widely studied in various domains. The resulting DAG typically represents a dynamic Bayesian network (DBN), capturing both the instantaneous and time-delayed relationships among variables of interest. We propose a new algorithm, IDYNO, to learn the DAG structure from potentially nonlinear time series data by using a continuous optimization framework that includes a continuous acyclicity constraint. The proposed algorithm is designed to handle both observational and interventional time series data. We demonstrate the promising performance of our method on synthetic benchmark datasets against state-of-the-art baselines. In addition, we show that the proposed method can more accurately learn the underlying structure of a sequential decision model, such as a Markov decision process, with a fixed policy in typical continuous control tasks.