Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus existing approaches invariably resort to time-discretisations which inevitably lead to approximations in inference. In this paper, we give the first general collection of methodologies for exact (in this context meaning discretisation-free) likelihood-based inference for discretely observed finite activity jump-diffusions. The only sources of error involved are Monte Carlo error and convergence of EM or MCMC algorithms. We shall introduce both frequentist and Bayesian approaches, illustrating the methodology through simulated and real examples.

翻译：对于离散观测的跳跃扩散过程进行统计推断是一个复杂问题，这引发了新的方法论挑战。现有方法均不可避免地依赖于时间离散化处理，从而导致推断过程存在近似误差。本文首次系统性地提出了一套通用方法论框架，用于对离散观测的有限活动跳跃扩散过程进行精确（在此上下文中指无离散化偏差的）似然推断。该方法仅存在蒙特卡洛误差以及期望最大化或马尔可夫链蒙特卡洛算法的收敛误差。我们将分别介绍频率学派和贝叶斯学派两种范式，并通过模拟案例与真实数据示例论证该方法的实用性。