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

Lixia Hu, Tao Huang and Jinhong You

Journal of the American Statistical Association, 2019, vol. 114, issue 527, 1191-1204

Abstract: 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. The financial data are also considered. Supplementary materials for this article are available online.

Date: 2019
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Citations: View citations in EconPapers (6)

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DOI: 10.1080/01621459.2018.1482753

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