Uncertain Threshold Autoregressive Model via LASSO Procedure

Uncertain time series models have been proposed to forecast future data based on imprecise known data. As an uncertain time series model, the uncertain threshold autoregressive model was proposed to deal with nonlinear data. The previous study estimated the unknown parameters in the uncertain threshold autoregressive model with the least-squares estimation. However, for nonlinear time series models, the least-squares estimation may cause overfitting of the model. To deal with this problem, this paper adds the least absolute shrinkage and selection operator penalty to the uncertain threshold autoregressive model to alleviate the level of overfitting. In addition, this paper uses the sum of square errors criterion to select the optimum order of the model. Finally, a real stock price example is provided to compare two different parameter estimation methods.