RATE OPTIMAL SEMIPARAMETRIC ESTIMATION OF THE MEMORY PARAMETER OF THE GAUSSIAN TIME SERIES WITH LONG‐RANGE DEPENDENCE
RATE OPTIMAL SEMIPARAMETRIC ESTIMATION OF THE MEMORY PARAMETER OF THE GAUSSIAN TIME SERIES WITH LONG‐RANGE DEPENDENCE
复制标题
长程相关高斯时间序列记忆参数的最优半参数估计
DOI：
10.1111/1467-9892.00038
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
A. Samarov
中科院分区：
文献类型：
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作者：
L. Giraitis;P. Robinson;A. Samarov
在长记忆时间序列模型中，存在几种记忆参数的估计器，其谱仅在零频率附近局部指定。本文给出了记忆参数的任意估计的极小极大风险的渐近下界，它是谱密度在零点的局部光滑度的函数。这个下界允许人们通过不同估计量的渐近行为来评估和比较它们，并声称任何达到这个下限的估计量都是速率最优的。一种对数周期图回归估计器，由Robinson(对数周期图回归)分析具有长期相关性的时间序列。安。统计一下。23(1995)，1048-72)，然后被证明达到下界，因此是速率最优的。
There exist several estimators of the memory parameter in long‐ memory time series models with the spectrum specified only locally near zero frequency. In this paper we give an asymptotic lower bound for the minimax risk of any estimator of the memory parameter as a function of the degree of local smoothness of the spectral density at zero. The lower bound allows one to evaluate and compare different estimators by their asymptotic behaviour, and to claim the rate optimality for any estimator attaining the bound. A log‐periodogram regression estimator, analysed by Robinson (Log‐periodogram regression of time series with long range dependence. Ann. Stat. 23 (1995), 1048‐‐72), is then shown to attain the lower bound, and is thus rate optimal.