Model Identification For Autoregressive Model Via The Coefficient Shrinkage

Model identification (i.e. selecting the lag order p) is a fundamental step in autoregressive modeling. Three coefficients shrinkage methods for the autoregressive model identification, the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and minimax concave penalty (MCP), were evaluated.Twelve different autoregressive models were generated via the Monte Carlo simulation. Various complications of the effect on autoregressive model identification, penalty function, model selection criteria, significance level, sample sizes, and coefficient dependency, were evaluated. The results of simulation show that several complications above have significantly effect. Specifically with regard to the accuracy of the identification of single complication, MCP was superior to SCAD and LASSO, BIC was superior to AIC and GCV, larger sample sizes was superior to smaller sample sizes. A optimal combination of model identification for autoregressive model via the coefficient shrinkage, MCP penalty+BIC criteria, was concluded. The accuracy of the combination was 76.4%. In order to select the model exactly, the combination of several methods is advised in real application.Meanwhile, in order to evaluate the effect in real application, the coefficient shrinkage was used in behavior data, and the result be compared with other author’s conclusion, the results of numerical simulation and the result of real application have the same conclusion. Therefore, we could draw the conclusion that the coefficient shrinkage method is a powerful method in model identification for autoregressive model.