This paper surveys state-of-the-art methods and models dedicated to time series analysis and modeling, with the final aim of prediction. This review aims to offer a structured and comprehensive view of the full process flow, and encompasses time series decomposition, stationary tests, modeling and forecasting. Besides, to meet didactic purposes, a unified presentation has been adopted throughout this survey, to present decomposition frameworks on the one hand and linear and nonlinear time series models on the other hand. First, we decrypt the relationships between stationarity and linearity, and further examine the main classes of methods used to test for weak stationarity. Next, the main frameworks for time series decomposition are presented in a unified way: depending on the time series, a more or less complex decomposition scheme seeks to obtain nonstationary effects (the deterministic components) and a remaining stochastic component. An appropriate modeling of the latter is a critical step to guarantee prediction accuracy. We then present three popular linear models, together with two more flexible variants of the latter. A step further in model complexity, and still in a unified way, we present five major nonlinear models used for time series. Amongst nonlinear models, artificial neural networks hold a place apart as deep learning has recently gained considerable attention. A whole section is therefore dedicated to time series forecasting relying on deep learning approaches. A final section provides a list of R and Python implementations for the methods, models and tests presented throughout this review. In this document, our intention is to bring sufficient in-depth knowledge, while covering a broad range of models and forecasting methods: this compilation spans from well-established conventional approaches to more recent adaptations of deep learning to time series forecasting.
翻译:本文调查了用于时间序列分析和建模的最先进的方法和模型,最后目的是预测。本论文旨在对全过程流提供结构化和全面的全过程流图,包括时间序列分解、固定测试、建模和预测。此外,为了达到教学目的,在整个调查中采用了统一演示,以提出单手和线性和非线性时间序列模型的分解框架。首先,我们破解了静态和线性之间的关系,并进一步研究了测试静态性的主要方法类别。接下来,时间序列分解的主要框架以统一的方式提出:取决于时间序列、固定测试、固定测试、建模和预测。此外,为了获得非静止效应(确定性组成部分)和其余的分解部分,对后者的适当建模是保证预测准确性的关键一步。然后,我们提出了三种受欢迎的线性模型,以及后两个更灵活的变体。在模型中,一个更接近于时间序列的更深层次的变体,仍然以统一的方式展示了时间序列分解的主要框架。 在整个网络中,我们提出了一套不固定的预估的模型,最近使用的是大量的模型,用来学习。