Regularization and variable selection for infinite variance autoregressive models |
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Authors: | Ganggang Xu Yanbiao Xiang Suojin Wang Zhengyan Lin |
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Affiliation: | 1. Department of Statistics, Texas A & M University, College Station, Texas 77843, USA;2. Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China |
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Abstract: | Autoregressive models with infinite variance are of great importance in modeling heavy-tailed time series and have been well studied. In this paper, we propose a penalized method to conduct model selection for autoregressive models with innovations having Pareto-like distributions with index α∈(0,2). By combining the least absolute deviation loss function and the adaptive lasso penalty, the proposed method is able to consistently identify the true model and at the same time produce efficient estimators with a convergence rate of n−1/α. In addition, our approach provides a unified way to conduct variable selection for autoregressive models with finite or infinite variance. A simulation study and a real data analysis are conducted to illustrate the effectiveness of our method. |
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Keywords: | Adaptive lasso Autoregressive model Infinite variance Least absolute deviation |
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