Selection of differencing order in autoregressive models based on the adaptive LASSO

We propose using the adaptive least absolute shrinkage and selection operator (LASSO) for selecting the differencing order of autoregressive models.The sparsity of the estimated coefficients from the adaptive LASSO naturally replaces the sequential significance tests employed by existing methods such as the augmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests.To fully leverage the adaptive LASSO, we also provide clear guidelines for obtaining the weights and selecting the tuning parameter.The final decision on the differencing order can be made by constructing a single regression coefficient path of the adaptive LASSO, which can be easily implemented using R and Python.Numerical studies through simulations and real data analyses are included to support the effectiveness of the adaptive LASSO.