Many central banks and government agencies use nowcasting techniques to obtain policy relevant information about the business cycle. Existing nowcasting methods, however, have two critical shortcomings for this purpose. First, in contrast to machine-learning models, they do not provide much if any guidance on selecting the best explantory variables (both high- and low-frequency indicators) from the (typically) larger set of variables available to the nowcaster. Second, in addition to the selection of explanatory variables, the order of the autoregression and moving average terms to use in the baseline nowcasting regression is often set arbitrarily. This paper proposes a simple procedure that simultaneously selects the optimal indicators and ARIMA(p,q) terms for the baseline nowcasting regression. The proposed AS-ARIMAX (Adjusted Stepwise Autoregressive Moving Average methods with exogenous variables) approach significantly reduces out-of-sample root mean square error for nowcasts of real GDP of six countries, including India, Argentina, Australia, South Africa, the United Kingdom, and the United States.