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.