Estimation of parameters of partially sinusoidal frequency model

In this paper, we propose a modification of the multiple sinusoidal model such that periodic data observed with the presence of a trend component can be analysed. In particular, we work with a linear trend model. But it can be developed similarly for the polynomial trend and the frequency model also. We consider the problem of estimation of frequency and amplitude parameters observed with a linear trend and a stationary linear process. We apply the usual least-squares method to the differenced data. It has been proved that the proposed estimators are strongly consistent and asymptotically normally distributed. Extensive simulations have been reported to justify the suitability of the model and the proposed method. One real data set, the monthly airline passenger data, has been analysed using the model. It is observed that the proposed model fits the data marginally better than the traditional time-series model in terms of residual sums of squares.