Varying-Coefficient Model and Applications for the Periodic Time Series

The time series in various kinds of fields not only exist a period but also easily affected by external variables of which the effect may vary with time. Sometimes, the period of some time series may be unknown. For the time series with unknown period and affected by external variables, we use a periodic varying-coefficient model to model it. We write the classical decomposition time series model as a partial linear varying-coefficient model with an unknown parameter. Then we approximate the varying-coefficient functions with B-spline and obtain the estimators of the period as well as the periodic sequence and the varying-coefficient functions in the decomposition model. The asymptotic behaviors of the estimators are given in our paper, including the consistency of period estimation and the asymptotic behavior of estimated periodic sequence and the varying-coefficient functions. We illustrate the superiority of our method through simulation studies in Section 4 and the applications to three real data examples including the number of the tourists in Hongkong and Macao and the crude oil price data in Section 5 show the utility of our method.