In this paper, the authors propose a method to obtain explicit solutions for simultaneous benchmarking and reconciliation problems for a system of variables when the cross-restrictions use time-varying coefficients. The method is based on a hierarchical Bayesian model with a normal-gamma specification for the prior distributions. The proposed solution provides explicit (not sequential) feasible estimations, including measurements for its statistical accuracy. One interesting feature of the proposed procedure is that it allows users to include one or several performance indicators and to estimate disaggregated values for incomplete years. The method is applied to obtain Quarterly Regional Accounts for the Spanish economy.

中文翻译：

---

随时间变化的交叉系数进行基准测试和协调

在本文中，作者提出了一种方法，当交叉限制使用时变系数时，该方法可以为变量系统的同时基准测试和协调问题获得显式解决方案。该方法基于分层贝叶斯模型，具有用于先验分布的正态伽马规范。所提出的解决方案提供了明确的（非顺序的）可行估计，包括对其统计准确性的测量。拟议程序的一个有趣特征是它允许用户包括一个或几个绩效指标，并估计不完整年份的分类值。该方法用于获取西班牙经济的季度区域账户。