变系数的周期性时间序列模型及其应用

Varying-Coefficient Model and Applications for the Periodic Time Series

存在于各个领域的时间序列不仅表现出周期性的特征还易受外界因素的影响,而且外界因素的影响并非一成不变,同时,部分时间序列的周期是未知的.对于这样的易受外界因素影响的周期性时间序列,本文旨在构造含有变系数函数的周期性序列模型.将经典的时间序列模型分解成一个含有未知参数的部分线性变系数模型,利用B样条逼近外生变量的变系数函数,借助带有l_(0)惩罚项的最小二乘回归得到未知周期、周期序列以及外生变量的影响系数的估计结果.本文还给出了估计量的理论性质,包括周期估计的相合性、周期序列估计和变系数函数估计的渐近性质.通过第4章的模拟,我们展现了本文方法的优越性.最后我们通过三个实际数据的应用展现了本文方法的实用性.

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.