Ten candidate models of the Auto-Regressive Moving Average (ARMA) family are investigated for representing and forecasting monthly and ten-day streamflow in three Indian rivers. The best models for forecasting and representation of data are selected by using the criteria of Minimum Mean Square Error (MMSE) and Maximum Likelihood (ML) respectively. The selected models are validated for significance of the residual mean, significance of the periodicities in the residuals and significance of the correlation in the residuals. The models selected, based on the ML criterion for the synthetic generation of the three monthly series of the Rivers Cauvery, Hemavathy and Malaprabha, are respectively AR(4), ARMA(2,1) and ARMA(3,1). For the ten-day series of the Malaprabha River, the AR(4) model is selected. The AR(1) model resulted in the minimum mean square error in all the cases studied and is recommended for use in forecasting flows one time step ahead.