论文标题
时间序列，反问题与球形模型之间的时间相关性之间的对应关系
Correspondence between temporal correlations in time series, inverse problems, and the Spherical Model
论文作者
论文摘要
在本文中，我们采用从统计力学到时间序列中时间相关的方法。我们提出了一种基于最大熵原理的方法，以生成限制的时间序列的合奏，以保留经验时间序列的时间结构的一部分。我们表明，对滞后的自相关的约束可以通过分析进行全面处理，并且对应于众所周知的铁磁体的球形模型。然后，我们扩展了这样的模型，以通过扰动理论对更复杂的时间相关性包含限制，这表明这在捕获方差中捕获滞后的一个自相关方面会大大改善。我们将方法应用于综合数据，并说明如何使用它来对数据生成过程的未来值提出期望。
In this paper we employ methods from Statistical Mechanics to model temporal correlations in time series. We put forward a methodology based on the Maximum Entropy principle to generate ensembles of time series constrained to preserve part of the temporal structure of an empirical time series of interest. We show that a constraint on the lag-one autocorrelation can be fully handled analytically, and corresponds to the well known Spherical Model of a ferromagnet. We then extend such a model to include constraints on more complex temporal correlations by means of perturbation theory, showing that this leads to substantial improvements in capturing the lag-one autocorrelation in the variance. We apply our approach on synthetic data, and illustrate how it can be used to formulate expectations on the future values of a data generating process.
