In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the diffusion process. Unlike typical time discretization approaches, such as psuedo-likelihood approximations with Shoji-Ozaki or Kessler's method, the CTMC approximation introduces no time-discretization error during parameter estimation, and is thus well-suited for typical econometric situations with infrequently sampled data. Due to the structure of the CTMC, we are able to obtain closed-form approximations for the sample likelihood which hold for general univariate diffusions. Comparisons of the state-discretization approach with approximate MLE (time-discretization) and Exact MLE (when applicable) demonstrate favorable performance of the CMTC estimator. Simulated examples are provided in addition to real data experiments with FX rates and constant maturity interest rates.

翻译：在本文中,我们提出了一个新的方法来估计参数扩散过程的参数。我们的方法基于一个封闭式的最大可能性估计器,用于对扩散过程进行近似连续时间标记链(CTMC),与典型的时间离散方法不同,如与Shoji-Ozaki或Kessler方法的Psuedo相似近似接近,CTMC近似在参数估计期间没有出现时间分解错误,因此适合不常见抽样数据的典型生态计量情况。由于CTMC的结构,我们能够获得用于一般单向扩散的样本可能性的封闭式近似值。国家分解方法与近似 MLE(时间分解)和Exact MLE(在适用时)的比较显示CMTC估计器的有利性性能。除了使用FX率和恒定成熟利率进行真实数据实验外,还提供模拟实例。