Time series often exhibit non-ergodic behaviour that complicates forecasting and inference. This article proposes a likelihood-based approach for estimating ergodicity transformations that addresses such challenges. The method is broadly compatible with standard models, including Gaussian processes, ARMA, and GARCH. A detailed simulation study using geometric and arithmetic Brownian motion demonstrates the ability of the approach to recover known ergodicity transformations. A further case study on the large macroeconomic database FRED-QD shows that incorporating ergodicity transformations can provide meaningful improvements over conventional transformations or naive specifications in applied work.

翻译：时间序列常呈现非遍历性行为，这给预测与统计推断带来困难。本文提出一种基于似然估计的遍历性变换方法以应对此类挑战。该方法与高斯过程、ARMA、GARCH等标准模型具有广泛的兼容性。通过几何布朗运动与算术布朗运动的详细仿真研究表明，本方法能够有效还原已知的遍历性变换。进一步基于宏观经济学大型数据库FRED-QD的案例研究显示，在应用研究中引入遍历性变换相比传统变换或朴素设定能带来显著改进。