Abstract

The Lévy-driven CARMA(2,1) process is a popular one with which to model stochastic volatility. However, there has been little development in statistical tools to verify this model assumption and assess the goodness-of-fit using high frequency realized volatility. When a Lévy-driven CARMA(2,1) is observed at high frequencies, the unobserved driving process can be approximated from the observed process. Since, under general conditions, the Lévy-driven CARMA(2,1) can be written as a sum of two dependent Lévy-driven CAR(1) process, the methods developed in Abdelrazeq, Ivanoff, and Kulik (2014, 2018) can be employed in order to use the approximated increments of the driving processes to test the assumption that the process is Lévy-driven. The performance of the tests is illustrated through simulation.

摘要

Lévy 驱动的 CARMA(2,1) 过程是一种流行的用于模拟随机波动率的过程。然而，在验证该模型假设和使用高频已实现波动率评估拟合优度的统计工具方面几乎没有发展。当在高频下观察到 Lévy 驱动的 CARMA(2,1) 时，未观察到的驱动过程可以从观察到的过程中近似。由于在一般条件下，Lévy-driven CARMA(2,1) 可以写成两个依赖的 Lévy-driven CAR(1) 过程的总和，因此 Abdelrazeq、Ivanoff 和 Kulik (2014, 2018) 开发的方法可以为了使用驱动过程的近似增量来测试过程是 Lévy 驱动的假设。通过仿真来说明测试的性能。