标题： 带有非线性约束的预测协调 显示英文标题

标题： Forecast reconciliation with non-linear constraints

摘要： 用于预测遵循线性约束的时间序列的方法近年来有了显著发展，尤其是随着预测调整方法的出现。 本文将预测调整扩展到非线性约束时间序列这一开放问题。 非线性约束可能出现在作为比率形成的变量中，例如死亡率和失业率。 在方法论方面，提出了非线性约束调整（NLCR）方法。 该算法以一种确保新预测满足约束的方式调整未能满足非线性约束的预测。 NLCR 方法是对非线性曲面的投影，被表述为一个约束优化问题。 在理论方面，再次使用优化方法，这次是为了推导出 NLCR 方法保证提高预测准确性的充分条件。 最后在实证方面，NLCR 被应用于人口学和经济学的两个数据集，并显示出相对于相关基准显著提高了预测准确性。 显示英文摘要

摘要： Methods for forecasting time series adhering to linear constraints have seen notable development in recent years, especially with the advent of forecast reconciliation. This paper extends forecast reconciliation to the open question of non-linearly constrained time series. Non-linear constraints can emerge with variables that are formed as ratios such as mortality rates and unemployment rates. On the methodological side, Non-linearly Constrained Reconciliation (NLCR) is proposed. This algorithm adjusts forecasts that fail to meet non-linear constraints, in a way that ensures the new forecasts meet the constraints. The NLCR method is a projection onto a non-linear surface, formulated as a constrained optimisation problem. On the theoretical side, optimisation methods are again used, this time to derive sufficient conditions for when the NLCR methodology is guaranteed to improve forecast accuracy. Finally on the empirical side, NLCR is applied to two datasets from demography and economics and shown to significantly improve forecast accuracy relative to relevant benchmarks.