Abstract In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP). Moreover, LLGMM is a dynamic non-parametric method. The DTIDMLSMVSP is an alternative approach to the GARCH(1,1) model, and it provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equations. Furthermore, applications of LLGMM to energy commodities price, U.S. Treasury Bill interest rate and the U.S.–U.K. foreign exchange rate data strongly exhibit its unique role, scope and performance, in particular, in forecasting and confidence-interval problems in applied statistics.

中文翻译：

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局部滞后自适应广义矩法：一种创新的估计和预测方法及其应用

摘要在这项工作中，尝试应用局部滞后自适应广义矩量法（LLGMM）估计随机微分动力学模型中的状态和参数。LLGMM的发展是受生物，化学，工程，能源商品市场，金融，医学，军事，物理科学和社会科学中连续时间非线性和非平稳随机动态模型验证问题中的参数和状态估计问题的推动。这种创新方法（LLGMM）的副产品是连续时间动态过程的模型规范和模型规定之间的平衡，以及局部样本均值和方差统计过程（DTIDMLSMVSP）的离散时间互连动态模型的开发。此外，LLGMM是一种动态的非参数方法。DTIDMLSMVSP是GARCH（1,1）模型的替代方法，它提供了一种迭代方案，用于在广义矩/观测方程的广义方法系统中更新统计系数。此外，将LLGMM应用于能源商品价格，美国国库券利率和美国-英国汇率数据，强烈展示了其独特的作用，范围和表现，尤其是在应用统计中的预测和置信区间问题上。