Determine The Order Of AR(p) Model Via Lasso

The predecessors already have done a lot about the problem of the regression coefficients in the AR(p) models. The estimation of the regression coefficients has many methods, including ordinary least squares, ridge regression ect. But a common shortcoming is that they do not produce sparse models. In order to solve this problem, Tibshirani(1996) proposed the Lasso, which will compress regression coefficient and set some regression coefficients to zero. This paper reviews the Lasso, and makes use of the Lasso method to carry on estimation of the regression coefficients in the AR(p) models. This paper also gives the calculation. This kind of method is more accurate and costs less time. Later, The paper does some simulations. End, this paper proves the asymptotic properties for the estimation, and uses the estimation method to deal with an example.