This paper develops and applies a method for directly estimating a multivariate, autoregressive moving-average (ARMA) model with mixed-frequency, time-series data. Unlike standard, single-frequency methods, the method does not require the data to be transformed to a single frequency (by temporally aggregating higher-frequency data to lower frequencies for interpolating lower-frequency data to higher frequencies) or the model to be restricted by frequency. Subject to computational constraints, the method can handle any number of variable and frequencies. In addition, variable can be treated as temporally aggregated and observed with errors and delays. The key to the method is to view lower-frequency data as periodically missing and to use the missing-data variant of the Kalman filter. In the application, a bivariate, ARMA model is estimated with monthly observations on total employment and quarterly observations on real GNP, in the U.S., for January 1958 to December 1978. The estimated model is, then, used to compute monthly forecasts of the variables for 1 to 12 months ahead, for January 1979 to December 1988. Compared with GNP forecasts, in particular, for similar periods produced by established econometric and time series models, present GNP forecasts are generally more accurate for 1 to 4 months ahead and about equally or slightly less accurate for 5 to 12 months ahead. The application, thus, shows that the present method is tractable and able to effectively exploit cross-frequency sample information, in ARMA estimate and forecasting, which standard methods cannot exploit at all.