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ARCH(0,1)系数中位无偏估计分布的渐近展开(英文)
引用本文:王德辉,Kanta Naito.ARCH(0,1)系数中位无偏估计分布的渐近展开(英文)[J].东北数学,2007(2).
作者姓名:王德辉  Kanta Naito
作者单位:School of Mathematics Jilin University,Department of Mathematics Shimane University Changchun,130012,Matsue,Japan,690-8504
基金项目:The NNSF(10571073)of China.
摘    要:This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1)coefficient.The exact distribution of the estimator can be easily derived,however its practical calculations are too heavy to implement, even though the middle range of sample sizes.Since the estimator is shown to have asymptotic normality,asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements.Accuracies of expansion formulas are evaluated numerically,and the results of which show that we can effectively use the expansion as a fine approximation of the distribution with rapid calculations.Derived expansion are applied to testing hypothesis of stationarity,and an implementation for a real data set is illustrated.


Asymptotic Expansion for the Distribution of a Median Unbiased Estimator of ARCH(0,1)Coefficient
WANG De-hui.Asymptotic Expansion for the Distribution of a Median Unbiased Estimator of ARCH(0,1)Coefficient[J].Northeastern Mathematical Journal,2007(2).
Authors:WANG De-hui
Abstract:This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1)coefficient.The exact distribution of the estimator can be easily derived,however its practical calculations are too heavy to implement, even though the middle range of sample sizes.Since the estimator is shown to have asymptotic normality,asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements.Accuracies of expansion formulas are evaluated numerically,and the results of which show that we can effectively use the expansion as a fine approximation of the distribution with rapid calculations.Derived expansion are applied to testing hypothesis of stationarity,and an implementation for a real data set is illustrated.
Keywords:ARCH(0  1)process  asymptotic distribution  Cornish-Fisher expansion  Edgeworth expansion  median unbiased
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