Abstract
In this paper, we study the estimation of the non-stationary time series in the presence of trend and period. We write the classical decomposition time series model as a partial linear model with an unknown parameter. Then we approximate the trend term with B-spline and obtain the estimators of the period, periodic sequence and trend. The asymptotic behaviors of the estimators are given in our paper, including the consistency of period estimation and the asymptotic behavior of the estimated periodic sequence and trend. We illustrate the superiority of our method through simulations and the applications to two real data examples show the utility of our method.
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