On instrumental variable estimation of sinusoid frequencies and the parsimony principle

Multiple sinusoids in noise can be modeled as an ARMA process with the AR parameters satisfying certain symmetry relations. According to the "parsimony principle" the constraints on the AR parameters should he taken into account to get improved estimation accuracy. It is shown in this note that when estimating the AR parameters by a general instrumental-variable method, such a parsimony does not necessarily apply. However, the parsimony principle does hold when an optimal instrumental-variable method is used.