Nonparametric estimation of time-changed Lévy models under high-frequency data
Nonparametric estimation of time-changed Lévy models under high-frequency data
复制标题
高频数据下时变Lévy模型的非参数估计
DOI：
10.1239/aap/1261669591
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发表时间：
2009
影响因子：
1.2
通讯作者：
José E. Figueroa
中科院分区：
文献类型：
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作者：
José E. Figueroa
设{Zt} t≥0是具有Lévy测度ν的Lévy过程，τ（t）=<$0 tr（u）du，其中{r（t）} t≥0是与Z无关的正遍历扩散.基于时变Lévy过程Xt φ（x）v（dx）的某些估计的渐近性质，这些估计又是几种非参数方法如筛基估计和核估计的基础.在r的二阶矩的一致有界性和标准短期遍历性质lim t→ 0 E φ（Zt）/t = β（φ）成立的条件下，当时间范围T以这样的方式增加，使得采样频率相对于T足够高时，保证了估计量的相合性和渐近正态性.
Let {Z t } t≥0 be a Lévy process with Lévy measure ν, and let τ(t)=∫0 t r(u) d u, where {r(t)} t≥0 is a positive ergodic diffusion independent from Z. Based upon discrete observations of the time-changed Lévy process X t ≔Z τt during a time interval [0,T], we study the asymptotic properties of certain estimators of the parameters β(φ)≔∫φ(x)ν(d x), which in turn are well known to be the building blocks of several nonparametric methods such as sieve-based estimation and kernel estimation. Under uniform boundedness of the second moments of r and conditions on φ necessary for the standard short-term ergodic property lim t→ 0 E φ(Z t )/t = β(φ) to hold, consistency and asymptotic normality of the proposed estimators are ensured when the time horizon T increases in such a way that the sampling frequency is high enough relative to T.