arXiv:2604.16865stat.MLcs.LG2026-04

从随机微分过程时间序列中提取有效统计特征,提升预测精度。

Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes

  • 用混合模型参数作为统计特征,通过均一与非均一方法重构漂移和扩散系数。
  • 非均一方法能捕捉系数随过程值变化的规律,相当于随机泰勒展开。
  • 在自回归预测中加入这些特征后,预测性能显著提升。

本文研究由未知随机漂移与扩散系数的Itô型随机微分方程生成的时间序列中,如何提取最具信息量的特征。仅利用原始时间序列本身的信息,不引入额外数据。为此,我们采用统计调整的混合型模型参数作为附加特征,其构造基于正态混合分布的统计分离技术。提出了两种系数重构方法:均一与非均一重构。前者不依赖当前过程值,后者考虑系数对过程值的依赖性,实际相当于时间序列的随机泰勒展开。通过在简单自回归预测算法中应用这些特征,验证了其有效性。为排除神经网络架构等干扰因素,未使用复杂模型,仅以基础自回归方法进行评估。结果表明,引入这些统计特征可显著提升预测性能。

原文摘要 · Abstract (English)

In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.

时间序列随机过程特征提取预测

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