Estimation and Identification of a Varying- Coefficient Additive Model for Locally Stationary Processes

尤进红教授， 加拿大女皇大学（University of Regina）统计学博士，美国北卡罗纳教堂山分校博士后， 上海财经大学统计与管理学院tenured常任轨教授、博士生导师和副院长，全国工业统计学教学研究会第九届理事会副会长，曾任Quality Technology and Quantitative Management (QTQM), special issue: Mathematical and Statistical Finance的客座编委（Guest Editor）。 尤进红教授有十余年的北美学习、工作经历。长期从事计量经济学、数理统计以及生物统计的科学研究； 在半参数，非参数回归建模，估计，检验及其在经济学， 金融学和生物医学方面的应用开展了许多有价值的研究工作；在国际和国内著名的统计和经济学杂志（包括Journal of the American Statistical Association，Journal of Econometric等）上发表学术论文六十余篇，其中三大检索论文四十余篇，被SCI他引几百余次；主持和参与过多个国家自科基金项目；为国际著名统计和计量经济杂志Annals of Statistics, Journal of the American Statistical Association , Biometrika和Journal of Econometric等的论文评审人。

The additive model and the varying-coefficient model are both powerful regression tools, with wide practical applications. However, our empirical study on a financial data has shown that both of these models have drawbacks when applied to locally stationary time series. For the analysis of functional data, Zhang and Wang have proposed a flexible regression method, called the varying-coefficient additive model (VCAM), and presented a two-step spline estimation method. Motivated by their approach, we adopt the VCAM to characterize the time-varying regression function in a locally stationary context. We propose a three-step spline estimation method and show its consistency and asymptotic normality. For the purpose of model diagnosis, we suggest an L2-distance test statistic to check multiplicative assumption, and raise a two-stage penalty procedure to identify the additive terms and the varying-coefficient terms provided that the VCAM is applicable. We also present the asymptotic distribution of the proposed test statistics, and demonstrate the consistency of the two-stage model identification procedure. Simulation studies investigating the finite sample performance of the estimation and model diagnosis methods confirm the validity of our asymptotic theory. A financial data is also considered.