Estimation for Nonnegative Lévy-Driven Ornstein-Uhlenbeck Processes
Estimation for Nonnegative Lévy-Driven Ornstein-Uhlenbeck Processes
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DOI：
10.1239/jap/1197908818
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发表时间：
2007-12
影响因子：
1
通讯作者：
P. Brockwell;R. Davis;Yu Yang
中科院分区：
文献类型：
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作者：
P. Brockwell;R. Davis;Yu Yang
连续时间自回归滑动平均（CARMA）过程是一类由非减Lévy过程驱动的非负核平稳非负连续时间过程。在金融计量经济学中，Barndorff-Nielsen和Shephard（2001）引入了由非减Lévy过程驱动的平稳Ornstein-Uhlenbeck（或CAR（1））过程，作为随机波动率的模型，以考虑各种可能的边际分布和跳跃的可能性。对于这样的过程，我们利用驱动Lévy过程增量的非负性，研究了当CAR（1）过程在均匀间隔时间0，h，.，Nh上的观测值可用时，参数的高效估计过程的性质.我们还展示了如何从一个连续观察到的实现过程中重建的背景驱动Lévy过程，并使用这个结果来估计的Lévy过程本身的增量时，h是小的。渐近性质的系数估计的推导和结果说明使用模拟伽马驱动的Ornstein-Uhlenbeck过程。
Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a very general class of stationary, nonnegative continuous-time processes. In financial econometrics a stationary Ornstein-Uhlenbeck (or CAR(1)) process, driven by a nondecreasing Lévy process, was introduced by Barndorff-Nielsen and Shephard (2001) as a model for stochastic volatility to allow for a wide variety of possible marginal distributions and the possibility of jumps. For such processes, we take advantage of the nonnegativity of the increments of the driving Lévy process to study the properties of a highly efficient estimation procedure for the parameters when observations are available of the CAR(1) process at uniformly spaced times 0,h,…,Nh. We also show how to reconstruct the background driving Lévy process from a continuously observed realization of the process and use this result to estimate the increments of the Lévy process itself when h is small. Asymptotic properties of the coefficient estimator are derived and the results illustrated using a simulated gamma-driven Ornstein-Uhlenbeck process.