A Least Squares Estimator for Lévy-driven Moving Averages Based on Discrete Time Observations
A Least Squares Estimator for Lévy-driven Moving Averages Based on Discrete Time Observations
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DOI：
10.1080/03610926.2012.763093
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
Shibin Zhang;Zhengyan Lin;Xinsheng Zhang
中科院分区：
文献类型：
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作者：
Shibin Zhang;Zhengyan Lin;Xinsheng Zhang
本文研究了Lévy驱动的移动平均的核函数参数θ的最小二乘估计（LSE），形式为X（t）=<$t− ∞K（θ（t-s））dL（s），其中是一个不含布朗运动部分的Lévy过程，K是核函数，θ > 0是参数.设h为两个连续观测值之间的时间跨度，n为样本的大小。当h → 0和nh → ∞时，研究了最小二乘估计的相合性和渐近正态性.最小二乘估计的小样本性能进行了评估，通过模拟实验。最后，两个实际数据的应用表明，列维驱动的移动平均线给出了一个很好的近似过程的自相关。
This article is concerned with a least squares estimator (LSE) of the kernel function parameter θ for a Lévy-driven moving average of the form X(t) = ∫t− ∞K(θ(t − s)) dL(s), where is a Lévy process without the Brownian motion part, K is a kernel function and θ > 0 is a parameter. Let h be the time span between two consecutive observations and let n be the size of sample. As h → 0 and nh → ∞, consistency and asymptotic normality of the LSE are studied. The small-sample performance of the LSE is evaluated by means of a simulation experiment. Finally, two real-data applications show that the Lévy-driven moving average gives a good approximation to the autocorrelation of the process.