SPECTRAL-ANALYSIS BASED ON THE CANONICAL AUTOREGRESSIVE DECOMPOSITION

Statistical inference for mixed spectral problems based on a parametri c time series model is studied, The model used herein is based on the canonical autoregressive decomposition (CARD) and represents the under lying random process as the sum of an autoregressive process and sinus oids, Maximum likelihood estimation of the unknown parameters in the m odel is considered. The entire estimation problem can be shown to requ ire a numerical maximization with respect to only the sinusoidal frequ encies, An iterative algorithm to efficiently implement this maximizat ion is presented. This enables us to examine a host of issues associat ed with a practical implementation of inferential procedures for mixed spectral problems. Some of the topics are accuracy of parameter estim ates, selection of model orders, and sensitivity and robustness of the spectral estimates to modeling inaccuracies. The modeling approach, t ogether with the inferential procedures, overcome many of the difficul ties encountered in current spectral estimation techniques.