One of the modern research lines in econometrics studies focuses on translating a wide variety of structural econometric models into their state-space form, which allows for efficient unknown dynamic system state and parameter estimations by the Kalman filtering scheme. The mentioned trend yields advanced state-space model structures, which demand innovative estimation techniques driven by application requirements to be devised. This article explores both the linear time-invariant multiple-input- multiple-output system (LTI MIMO) and the pairwise Markov model (PMM) with the related pairwise Kalman filter (PKF). In particular, we design robust gradient-based adaptive Kalman-like filtering methods for the simultaneous state and parameter estimation in the outlined model structures. Our methods are fast and accurate because their analytically computed gradient is utilized in the calculation instead of its numerical approximation. Also, these employ the numerically robust UDUT-factorization-based Kalman filter implementation, which is reliable in practice. Our novel techniques are examined on numerical examples and used for treating one stochastic model in econometrics.

中文翻译：

---

基于 UD 的成对和 MIMO 卡尔曼滤波用于计量经济模型结构的估计


计量经济学研究的现代研究方向之一侧重于将各种结构计量经济学模型转化为其状态空间形式，从而允许通过卡尔曼滤波方案进行有效的未知动态系统状态和参数估计。上述趋势产生了先进的状态空间模型结构，这需要设计由应用需求驱动的创新估计技术。本文探讨了线性时不变多输入多输出系统 (LTI MIMO) 和具有相关成对卡尔曼滤波器 (PKF) 的成对马尔可夫模型 (PMM)。特别是，我们设计了鲁棒的基于梯度的自适应卡尔曼滤波方法，用于在概述的模型结构中同时进行状态和参数估计。我们的方法快速且准确，因为在计算中使用了分析计算的梯度而不是数值近似。此外，它们还采用基于 UDUT 分解的数值鲁棒卡尔曼滤波器实现，这在实践中是可靠的。我们的新技术通过数值例子进行了检验，并用于处理计量经济学中的一个随机模型。