This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain to capture regime changes, enabling a more realistic representation of evolving market conditions or environmental factors. Although the continuous dynamics are typically observable, the hidden nature of the Markov chain introduces significant complexity, rendering standard likelihood-based methods less effective. To address these challenges, we propose an estimation algorithm designed for discrete, high-frequency observations, even when the Markov chain is not directly observed. Our approach integrates the Expectation-Maximization (EM) algorithm, which iteratively refines parameter estimates in the presence of latent variables, with a quasi-likelihood method adapted to NIG noise. Notably, this method can simultaneously estimate parameters within both the SDE coefficients and the driving noise. Simulation results are provided to evaluate the performance of the algorithm. These experiments demonstrate that the proposed method provides reasonable estimation under challenging conditions.

翻译：本文研究由正态逆高斯噪声驱动的体制转换随机微分方程的参数估计问题。所考虑的模型引入连续时间有限状态马尔可夫链以捕捉体制转换，从而能够更真实地刻画市场条件或环境因素的动态演化。尽管连续动态过程通常可观测，但马尔可夫链的隐状态特性带来了显著复杂性，使得传统的基于似然函数的方法难以奏效。为应对这些挑战，我们提出一种适用于离散高频观测数据的估计算法，该算法在马尔可夫链不可直接观测时仍能有效工作。本方法将适用于潜变量迭代参数优化的期望最大化算法，与适配于正态逆高斯噪声的拟似然估计相结合。值得注意的是，该方法能同时估计随机微分方程系数与驱动噪声中的参数。我们通过仿真实验评估算法性能，结果表明所提方法在挑战性条件下仍能提供合理的参数估计。