Time series observed at different temporal scales cannot be simultaneously analyzed by traditional multivariate time series methods. Adjustments must be made to address issues of asynchronous observations. For example, many macroeconomic time series are published quarterly and other price series are published monthly or daily. Common solutions to the analysis of asynchronous time series include data aggregation, mixed frequency vector autoregressive models, and factor models. In this research, I set up a systematic approach to the analysis of asynchronous multivariate time series based on an approximate dynamic factor model. The methodology treats observations of various temporal frequencies as contemporaneous series. A two-step model estimation and identification scheme is proposed. This method allows explicit structural restrictions that account for appropriate temporal ordering of the mixed frequency data. The methodology consistently estimates the dynamic factors, however, no prior knowledge on the factors is required. To ensure a computationally efficient robust algorithm and model specification, I make use of modern penalized likelihood methodologies. The fitted model captures the effects of temporal relationships across the asynchronous time series in an interpretable manner. The methodology is studied through simulation and applied to several examples. The simulations and examples demonstrate good performance in model specification, estimation and out-of-sample forecasting.