ASYMPTOTIC THEORY OF THE LEAST-SQUARES ESTIMATORS OF SINUSOIDAL SIGNAL

The consistency and the asymptotic normality of the least squares esti mators are derived of the sinusoidal model under the assumption of sta tionary random error. It is observed that the model does not satisfy t he standard sufficient conditions of Jennrich (1969), Wu (1981) or Kun du (1991). Recently the consistency and the asymptotic normality are d erived for the sinusoidal signal under the assumption of normal error (Kundu; 1993) and under the assumptions of independent and identically distributed random variables in Kundu and Mitra (1996). This paper wi ll generalize them. Hannan (1971) also considered the similar kind of model and establish the result after making the Fourier transform of t he data for one parameter model. We establish the result without makin g the Fourier transform of the data. We give an explicit expression of the asymptotic distribution of the multiparameter case, which is not available in the literature. Our approach is different from Hannan's a pproach. We do some simulations study to see the small sample properti es of the two types of estimators.