Time-varying coefficient models are important tools in time series analysis due to their flexibility to fit non-stationary data. To improve the accuracy of these models, it is important to identify covariates with null, constant and time-varying effects and to estimate their coefficients. This article proposes a combination of the local linear smoothing method and the adaptive group lasso penalty approach to achieve covariate identification and coefficient estimation. The penalty term consists of two parts. The first term penalizes the norm of the coefficient function, which is used to select relevant variables. The second term penalizes the norm of the derivative function, which assesses the constancy of the coefficient functions. The asymptotic properties of the proposed methodology are established. Performance of the proposed method is demonstrated using simulated data along with an application to the analysis of the air quality and health data in Hong Kong.

中文翻译：

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时变系数模型的同时变量选择和结构识别

时变系数模型是时间序列分析中的重要工具，因为它们可以灵活地拟合非平稳数据。为了提高这些模型的准确性，识别具有零效应、恒定效应和时变效应的协变量并估计它们的系数非常重要。本文提出结合局部线性平滑法和自适应组套索惩罚法来实现协变量识别和系数估计。处罚期限由两部分组成。第一项惩罚系数函数的范数，用于选择相关变量。第二项惩罚导数函数的范数，它评估系数函数的恒定性。建立了所提出方法的渐近特性。