Efficient estimation of stable Levy process with symmetric jumps
Efficient estimation of stable Levy process with symmetric jumps
复制标题
具有对称跳跃的稳定 Levy 过程的有效估计
DOI：
10.1007/s11203-018-9181-0
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发表时间：
2018
影响因子：
0.8
通讯作者：
Alexandre Brouste and Hiroki Masuda
中科院分区：
文献类型：
--
作者：
Ajay Jasra;Kengo Kamatani and Hiroki Masuda;Alexandre Brouste and Hiroki Masuda
研究了具有高频漂移和对称跳跃的非高斯平稳Lévy过程的有效估计问题。对于这一统计实验，利用非对角赋范矩阵证明了非奇异Fisher信息矩阵似然的局部渐近正态分布。并证明了相关似然方程的根序列的渐近正态和有效性。此外，我们还证明了一个简单的初级矩方法可以用来作为评分过程的初始估计器，从而使我们能够方便地绕过数值要求高的似然优化。我们的模拟结果表明，一步估计可以表现出与最大似然估计非常相似的有限样本性能。
Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator.