Least Squares Volatility Change Point Estimation for Partially Observed Diffusion Processes
Least Squares Volatility Change Point Estimation for Partially Observed Diffusion Processes
复制标题
部分观测扩散过程的最小二乘波动率变化点估计
DOI：
10.1080/03610920801919692
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
S. Iacus
中科院分区：
文献类型：
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作者：
A. Gregorio;S. Iacus
假设一维扩散过程X = {X t, 0≤t≤t}，漂移量b(X)，扩散系数已知至θ > 0，在t*∈(0,t)的某点切换波动状态。在X的离散时间观测的基础上，问题是估计波动结构t*的变化瞬间以及变化点前后θ的两个值，即θ1和θ2。假设采样发生在长度为Δ n的规则间隔时间内，nΔ n = t。为了解决我们的统计问题，我们使用最小二乘方法。给出了高频格式下估计量的一致性、收敛率和分布结果。我们还研究了具有未知漂移和未知挥发性但恒定的扩散过程。
A one-dimensional diffusion process X = {X t , 0 ≤ t ≤ T}, with drift b(x) and diffusion coefficient known up to θ > 0, is supposed to switch volatility regime at some point t* ∈ (0,T). On the basis of discrete time observations from X, the problem is the one of estimating the instant of change in the volatility structure t* as well as the two values of θ, say θ1 and θ2, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length Δ n with nΔ n = T. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant.