Estimating the order of multiple sinusoids model using exponentially embedded family rule: Large sample consistency

In this paper, we consider the problem of estimating the number of components of a superimposed multiple sinusoids model. We study the large sample asymptotic properties of the Exponentially Embedded Family (EEF) based method for estimation of the order of the multiple sinusoids model. We establish that the estimator of model order using the EEF rule is large sample consistent. Finite sample simulation examples are presented to compare the performance of the EEF rule with three commonly used information criterion based methods.