Two-step variable selection in partially linear additive models with time series data |
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Authors: | Mu Feng Ximing Cheng |
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Institution: | 1. Department of Statistics and Finance, University of Science and Technology of China, Anhui, P. R. China;2. Department of Statistics, Beijing Information Science and Technology University, Beijing, P. R. China |
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Abstract: | Lots of semi-parametric and nonparametric models are used to fit nonlinear time series data. They include partially linear time series models, nonparametric additive models, and semi-parametric single index models. In this article, we focus on fitting time series data by partially linear additive model. Combining the orthogonal series approximation and the adaptive sparse group LASSO regularization, we select the important variables between and within the groups simultaneously. Specially, we propose a two-step algorithm to obtain the grouped sparse estimators. Numerical studies show that the proposed method outperforms LASSO method in both fitting and forecasting. An empirical analysis is used to illustrate the methodology. |
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Keywords: | Adaptive LASSO Additive models GCV Group LASSO Orthogonal series approximation Variable selection |
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