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We derive the Cramer-Rao bound for the parameters of a general time series model whose parameterization is dependent upon an unknown integer model order. To illustrate the usefulness of the theoretical results, the example of autoregressive spectral density estimation using Akaike (1974) order selection criterion is presented.
Estimating the parameters for a constant amplitude, polynomial-phase signal with additive Gaussian noise is considered. The difficulty in this problem is that there are many unobserved integers when a linear regression model is used for wrapped phases [I]. Analysing the least squares target function based on the regression model, we use the differencing… (More)