Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet most time-series analysis methods that are used in practice, on important problems across science and industry, make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here we review and unify a diverse literature of algorithms for PINUP. We formulate the problem, and categorize the various algorithmic contributions. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on - notably the non-stationary Lorenz process and logistic map - are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.

非平稳系统在世界上随处可见，需要分析非平稳过程的方法很多，但大多数时序分析方法都是基于平稳性的假设，而一个关键问题是从观察到的时间序列中推断参数，而无需了解或推断出底层系统的数学模型。我们在这里对PINUP问题的算法进行了综述和统一，纳入了各种算法贡献，并提出了更具挑战性的问题，以推动该领域的方法学进展和对非平稳现象的研究。

从非平稳未知过程中推断参数