Quasi-maximum exponential likelihood estimator and portmanteau test of double AR ( p ) $\operatorname{AR}(p)$ model based on Laplace ( a , b ) $\operatorname{Laplace}(a,b)$

The paper studies the estimation and the portmanteau test for double \(\operatorname{AR}(p)\) model with \(\operatorname{Laplace}(a,b)\) distribution. The double \(\operatorname{AR}(p)\) model is investigated to propose firstly the quasi-maximum exponential likelihood estimator, design a portmanteau test of double \(\operatorname{AR}(p)\) on the basis of autocorrelation function, and then establish some asymptotic results. Finally, an empirical study shows that the estimation and the portmanteau test obtained in this paper are very feasible and more effective.