Spectral analysis based on the canonical autoregressive decomposition

Statistical inference for mixed spectral problems based on a parametric time series model is studied. The model used is based on the canonical autoregressive decomposition (CARD) and represents the underlying random process as the sum of an autoregressive process and sinusoids. Maximum likelihood estimation of the unknown parameters in the model is considered. The entire estimation problem can be shown to require a numerical maximization with respect to only the sinusoidal frequencies. An iterative algorithm to efficiently implement this maximization is presented. This enables us to examine a host of issues associated with a practical implementation of inferential procedures for mixed spectral problems. Some of the topics are accuracy of parameter estimates, selection of model orders, and sensitivity and robustness of the spectral estimates to modeling inaccuracies. The modeling approach, together with the inferential procedures, overcome many of the difficulties encountered in current spectral estimation techniques.