Estimation for Non-Negative Lévy-Driven CARMA Processes
研究了非负Lévy驱动的连续时间自回归移动平均(CARMA)过程的参数估计方法，将高阶过程分解为相依的Ornstein-Uhlenbeck过程之和，适用于随机波动建模。
Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a useful and very general class of stationary, nonnegative continuous-time processes that have been used, in particular, for the modeling of stochastic volatility. Brockwell, Davis, and Yang (2007) derived efficient estimates of the parameters of a nonnegative Lévy-driven CAR(1) process and showed how the realization of the underlying Lévy process can be estimated from closely-spaced observations of the process itself. In this article we show how the ideas of that article can be generalized to higher order CARMA processes with nonnegative kernel, the key idea being the decomposition of the CARMA process into a sum of dependent Ornstein--Uhlenbeck processes.