Statistics and Its Interface

Volume 4 (2011)

Number 2

Threshold variable selection via a $L_1$ penalty approach

Pages: 137 – 148



Qian Jiang (Department of Mathematics and Statistics, Guizhou College of Finance and Economics, China)

Yingcun Xia (Department of Statistics and Applied Probability, Risk Management Institute, National University of Singapore)


Selecting the threshold variable is a key step in building a general threshold autoregressive (TAR) model. Based on a general smooth threshold autoregressive (STAR) model, we propose to select the threshold variable by the recently developed $L_1$-penalizing approach. Moreover, by penalizing the direction of the coefficient vector instead of the coefficients themselves, the threshold variable is more accurately selected. Oracle properties of the estimator are obtained. Its advantage is shown with both numerical and real data analysis.


smooth threshold AR model, variable selection, adaptive lasso, oracle property

Published 22 June 2011