A note on estimation by least squares for harmonic component models

Let observations (X_1, H ,X_n) be generated by a harmonic model such that X_t=A_0 cos omega_0t + B_0 sin omega_0t + epsilon _t, where A_0,B_0, omega_0 are constants and ( epsilon _t) is a stationary process with zero mean and finite variance. The estimation of A_0,B_0, omega_0 by the method of least squares is considered. It is shown that, without any restriction on omega in the minimization procedure, the estimate is an n-consistent estimate of omega_0, and hence ( ) has the usual asymptotic distribution. Copyright 2003 Blackwell Publishing Ltd.