论文标题
多元Lévy驱动的Ornstein-Uhlenbeck的校准，并应用于弱从属
Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination
论文作者
论文摘要
考虑一个多元lévy驱动的Ornstein-Uhlenbeck过程，其中固定分布或背景驱动lévy过程来自参数家族。假设创新术语是绝对连续的，我们得出了可能性函数。详细研究了两个示例：通过弱方差alpha-gamma过程给出了固定分布或背景驱动过程的过程，这是对使用弱下属创建的方差伽马过程的多元概括。在前一种情况下，我们对背景驱动过程的明确表示，导致创新术语是离散和连续的混合物，允许对过程的精确模拟以及单独的可能性函数。在后一种情况下，我们表明创新术语绝对是连续的。模拟研究的结果表明，使用傅立叶反演计算的最大似然可用于准确估计两种情况下的参数。
Consider a multivariate Lévy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving Lévy process is from a parametric family. We derive the likelihood function assuming that the innovation term is absolutely continuous. Two examples are studied in detail: the process where the stationary distribution or background driving Lévy process is given by a weak variance alpha-gamma process, which is a multivariate generalisation of the variance gamma process created using weak subordination. In the former case, we give an explicit representation of the background driving Lévy process, leading to an innovation term which is discrete and continuous mixture, allowing for the exact simulation of the process, and a separate likelihood function. In the latter case, we show the innovation term is absolutely continuous. The results of a simulation study demonstrate that maximum likelihood numerically computed using Fourier inversion can be applied to accurately estimate the parameters in both cases.
