时间序列中长期预测的5种常用策略

时间序列中长期预测的5种常用策略


A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition

基于NN5预测竞赛的多步时间序列预测策略的综述和比较


综述类论文

期刊:Expert Systems with Applications

中科院分区:2区

2018年影响因子(IF):4.292

目前Google Scholar被引:231次


0. Abstract:

1. Multi-step ahead forecasting is still an open challenge in time series forecasting. 2. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. 3. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. 4. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). 5. In addition, we considered the effects of deseasonalization, input variable selection, and forecast combination on these strategies and on multi-step ahead forecasting at large. 6. The following three findings appear to be consistently supported by the experimental results: Multiple-Output strategies are the best performing approaches, deseasonalization leads to uniformly improved forecast accuracy, and input selection is more effective when performed in conjunction with deseasonalization.


1. 在时间序列预测中,多步预测仍然是一个开放的挑战。2. 文献中已经提出了几种处理这一复杂问题的方法,但是对大量任务的广泛比较仍然缺乏。3. 本文旨在通过回顾现有的多步预测策略,并从理论和实践方面上进行比较,从而填补这一空白。4. 为了达到这个目标,我们使用一个大型的实验基准(即来自NN5预测竞赛的111系列)对这些不同的策略进行了大规模的比较。5. 此外,我们还考虑了去季节化、输入变量选择和预测组合对这些策略和多步预测的影响。6. 实验结果一致地支持以下三个结论:多输出策略是最有效的方法,去季节化可以提高预测精度。当与去季节化一起执行时,输入变量选择会变得更有效。


1. Introduction:

提出了5种时间序列多步预测的策略,分别为:Recursive (递归策略),Direct(直接策略),DirRect(直接预测和递归预测相结合),MIMO(多输入多输出)和DIRMO(直接多输出)。


2. Strategies for multi-step-ahead time series forecasting

多步预测又称为长期预测,其含义是运用历史的时间序列[y1, ..., yN]预测之后的H步序列[yN+1, ..., yN+H],其中N表示已观测数据的个数,H>1表示预测范围。


2.1 Recursive strategy

也被称为Iterated strategy,单步预测模型可以表示为

y_{t+1}=f\left(y_{t}, \ldots, y_{t-d+1}\right)+w

其中d表示时间窗的长度(输入到模型中时间序列的长度),t[d, …, N-1]

故单步预测过程可定义为

\hat{y}_{N+h}=\left\{\begin{array}{ll}{\hat{f}\left(y_{N}, \ldots, y_{N-d+1}\right)} & {\text { if } h=1} \\ {\hat{f}\left(\hat{y}_{N+h-1}, \ldots, y_{N+1}, y_{N}, \ldots, y_{N-d+h}\right)} & {\text { if } h \in[2, \ldots, d]} \\ {\hat{f}\left(\hat{y}_{N+h-1}, \ldots, \hat{y}_{N+h-d}\right)} & {\text { if } h \in[d+1, \ldots, H]}\end{array}\right.

缺点:将预测值作为输入数据时,误差会累积。


2.2 Direct strategy

也被称为Independent strategy。与循环预测不同,它不再通过单步迭代得到多步后的结果,而是直接建立一个多步映射关系。预测模型可以表示为

y_{t+h}=f_{h}\left(y_{t}, \ldots, y_{t-d+1}\right)+w

预测过程可定义为

\hat{y}_{N+h}=\hat{f}_{h}\left(y_{N}, \ldots, y_{N-d+1}\right)

缺点:需要M步预测时,需要训练M个模型,因此计算量大。


2.3 DirRec strategy

Recursive strategyDirect strategy相结合,预测模型可以表示为

y_{t+h}=f_{h}\left(y_{t+h-1}, \ldots, y_{t-d+1}\right)+w

预测过程可定义为

\hat{y}_{N+h}=\left\{\begin{array}{ll}{\hat{f}_{h}\left(y_{N}, \ldots, y_{N-d+1}\right)} & {\text { if } h=1} \\ {\hat{f}_{h}\left(\hat{y}_{N+h-1}, \ldots, \hat{y}_{N+1}, y_{N}, \ldots, y_{N-d+1}\right)} & {\text { if } h \in[2, \ldots, H]}\end{array}\right.

值的注意的是,输入数据的长度是变化的。预测一步的时候,输入数据长度为d;预测h步的时候,输入数据长度变为d+h


2.4 MIMO strategy

Recursive strategyDirect strategyDirRec strategy都只考虑到了单目标输出,而MIMO (multiple input multiple output)strategy顾名思义,是一个多目标输出的过程。预测模型可以表示为

\left[y_{t+H}, \ldots, y_{t+1}\right]=F\left(y_{t}, \ldots, y_{t-d+1}\right)+w

预测过程可定义为

\left[\hat{y}_{N+H}, \ldots, \hat{y}_{N+1}\right]=\hat{F}\left(y_{N}, \ldots, y_{N-d+1}\right)

该策略避免了Direct strategy的条件独立性假设,也避免了Recursive strategy所面临的误差累积。但是MIMO strategy有一个缺点,它使预测模型的结构变得一致,这种约束大大降低了预测方法的灵活性。


2.5 DIRMO strategy

DIRMO strategy结合了Direct strategyMIMO strategy的特点,预测模型可以表示为

\left[y_{t+p^{*} s}, \ldots, y_{t+(p-1)^{*} s+1}\right]=F_{p}\left(y_{t}, \ldots, y_{t-d+1}\right)+w

预测过程可定义为

\left[\hat{y}_{N+p^{*} s}, \ldots, \hat{y}_{N+(p-1)^{*} s+1}\right]=\hat{F}_{p}\left(y_{N}, \ldots, y_{N-d+1}\right)

本质上就是将H步预测分成了s段,Direct strategy需要训练h个模型,MIMO strategy需要训练1个模型,而DIRMO strategy需要训练H/s个模型。(个人感觉没啥噱头!)




通过表1和表2一下就可以看出五种方法的区别了,这就是现在时间序列中长期预测常见的5种策略。

论文的其余部分没啥亮点,有兴趣的同学可以自行下载阅读。

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发布于 2019-09-30 21:19