This thesis deals with multivariate autoregressive systems in the case of observations with different sampling rates, the so-called mixed-frequency (MF) observations. In this work the case where the output variable can be separated into a fast (high-frequency) and a slow (low-frequency) component will be given attention. An example of such an observation scheme would be a two-dimensional time series in which the first component is observed monthly, for instance unemployment, and the second quarterly, for instance GDP. It is assumed that the underlying system generates the output at each time point, the so-called high-frequency, however, the output of the slow component is only observed at an integer multiple of the high-frequency. It is worth mentioning that the mixed-frequency case assumes a uniform observation pattern. This special observation pattern plays an important role in high-dimensional time series, where the availability of the univariate time series is given at different sampling rates. A popular approach to model high-dimensional time series are the generalized linear dynamic factor models, where the static factors can be typically modeled by a singular autoregressive system. A central part of this thesis is concerned with identifiability and with the asymptotic behavior of parameter estimators of the high-frequency autoregressive system given mixed-frequency observations. Here two cases for the slow component are considered: the stock and the flow case. It turns out that not all systems are identifiable, however, a large subset of the parameter space is still identifiable. Due to missing observations certain autocovariances cannot be observed and thus the standard Yule-Walker equations for the estimation cannot be used. Therefor the extended Yule-Walker (XYW) equations are introduced. These XYW equations represent, in a certain sense, the mixed-frequency analogue to the standard Yule-Walker equations. Furthermore, the XYW estimator and the generalized method of moments estimator (GMM) are discussed and it is shown that they are asymptotically normal under certain assumptions. In order to achieve this, a generalization of Bartlett's formula for the mixed-frequency case is required. Also the maximum likelihood (ML) estimator is treated and the exact asymptotic variance for the special AR (1) case is derived. As shown by examples, the GMM estimator is, in general, not asymptotically efficient. In addition, some finite sample properties are investigated through simulations.