序约束下ARCH模型的最小二乘估计

Least Square Estimation about the ARCH Model under Ordered Restriction

研究序约束条件下自回归条件异方差(ARCH)模型的统计推断. 给出ARCH(q)模型中非负参数(α0,α1,α2,…,αq)的一种最小二乘估计的准则函数, 证明了由此得到参数估计的强相合性. 而且通过讨论在序约束(α1≥α2≥…≥αq)下估计的准确形式及其渐近性, 得到了检验统计量的形式, 从而解决了在参数空间有序约束条件下的假设检验问题.

This paper deals with the statistical inference of an autoregressive conditional heteroscedasticity (ARCH) model under restriction. We gave a criteria function to compute a least squares estimation for the nonnegative parameters (α_0,α_1,α_2,…,α_q) of the ARCH model, and showed the strong consistency of the estimation . By discussing the exact expression and the asymptotic normality of the estimation under ordered restriction (α_1≥α_2≥…≥α_q), we obtained the form of the test statistical quantity, then solved the testing problem with the parameter space under ordered restriction.