An application of a BIC-type method to harmonic analysis and a new criterion for order determination of an AR process

A classical problem in harmonic analysis is discussed that arises when the periods are divisors of the series length and the disturbance noise is white Gaussian. An approach is presented whereby the presence or absence of the harmonics is determined by a method of the Bayesian information criterion (BIC) type. The criterion is derived based on the theory of statistics of extremes. A Hopfield neural network implementation of the scheme is shown and some simulation results are presented to demonstrate the effectiveness of the method. The above idea is applied to the order determination problem of an autoregressive (AR) process. Relations between the criterion presented and other existing ones, such as the usual BIC and the criterion of by E.J. Hannan and B.G. Quinn (see J. Roy. Statist. Soc., Ser. B, vol.41, p.190-5, 1979), are clarified