VALID EDGEWORTH EXPANSIONS FOR THE WHITTLE MAXIMUM LIKELIHOOD ESTIMATOR FOR STATIONARY LONG-MEMORY GAUSSIAN TIME SERIES
平稳长记忆高斯时间序列中 Whittle 最大似然估计量的有效 Edgeworth 展开
In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter . The error of the ( s − 2)-order expansion is shown to be o ( n −( s −2)/2 )—the usual independent and identically distributed rate—for a wide range of models, including the popular ARFIMA( p , d , q ) models. The expansion is valid under mild assumptions on the behavior of the…