Statistical inference for mixed spectral problems based on a parametric time series is studied. The model used here, called the CARD model, represents the underlying random process as the sum of an autoregressive process and sinusoids. An iterative algorithm to implement efficiently the maximum likelihood estimator of the unknown model parameters is presented. This enables investigation of practical issues such as accuracy of parameter estimates, selection of model orders, and sensitivity and robustness of the spectral estimates to modeling inaccuracies.<>