序约束下ARCH模型的最小二乘估计

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,…, α_q)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≥…≥α_q)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.

Least Square Estimation about the ARCH Model under Ordered Restriction

This paper deals with the statistical inference of an au toregressive conditional heteroscedasticity (ARCH) model under restriction. We g ave a criteria function to compute a least squares estimation for the nonnegativ e parameters (α₀,α₁,α₂,…,α_q) of the ARCH model, and showed the strong consistency of the estimation. By discuss ing the exact expression and the asymptotic normality of the estimation under ordered restriction (α₁≥α₂≥…≥α_q), we obtained the form of the test statist ical quantity, then solved the testing problem with the parameter space under or dered restriction.