Long-term time series forecasting (LTSF) represents a critical frontier in
time series analysis, distinguished by its focus on extensive input sequences,
in contrast to the constrained lengths typical of traditional approaches. While
longer sequences inherently convey richer information, potentially enhancing
predictive precision, prevailing techniques often respond by escalating model
complexity. These intricate models can inflate into millions of parameters,
incorporating parameter-intensive elements like positional encodings,
feed-forward networks and self-attention mechanisms. This complexity, however,
leads to prohibitive model scale, particularly given the time series data's
semantic simplicity. Motivated by the pursuit of parsimony, our research
employs conditional correlation and auto-correlation as investigative tools,
revealing significant redundancies within the input data. Leveraging these
insights, we introduce the HDformer, a lightweight Transformer variant enhanced
with hierarchical decomposition. This novel architecture not only inverts the
prevailing trend toward model expansion but also accomplishes precise
forecasting with drastically fewer computations and parameters. Remarkably,
HDformer outperforms existing state-of-the-art LTSF models, while requiring
over 99\% fewer parameters. Through this work, we advocate a paradigm shift in
LTSF, emphasizing the importance to tailor the model to the inherent dynamics
of time series data-a timely reminder that in the realm of LTSF, bigger is not
invariably better.

通过条件相关性和自相关性作为研究工具，我们引入了一种轻量级的 HDformer 模型，该模型使用分层分解技术，不仅推翻了模型扩展的趋势，而且在大量减少计算和参数的同时实现了精确的长期时间序列预测，超越了现有的最先进模型，表明在长期时间序列预测中，模型的大小并不一定更好。

长期时间序列预测中的有效模型规模再思考

The Bigger the Better? Rethinking the Effective Model Scale in Long-term  Time Series Forecasting

Recently, there has been a surge of Transformer-based solutions for the
long-term time series forecasting (LTSF) task. Despite the growing performance
over the past few years, we question the validity of this line of research in
this work. Specifically, Transformers is arguably the most successful solution
to extract the semantic correlations among the elements in a long sequence.
However, in time series modeling, we are to extract the temporal relations in
an ordered set of continuous points. While employing positional encoding and
using tokens to embed sub-series in Transformers facilitate preserving some
ordering information, the nature of the \emph{permutation-invariant}
self-attention mechanism inevitably results in temporal information loss. To
validate our claim, we introduce a set of embarrassingly simple one-layer
linear models named LTSF-Linear for comparison. Experimental results on nine
real-life datasets show that LTSF-Linear surprisingly outperforms existing
sophisticated Transformer-based LTSF models in all cases, and often by a large
margin. Moreover, we conduct comprehensive empirical studies to explore the
impacts of various design elements of LTSF models on their temporal relation
extraction capability. We hope this surprising finding opens up new research
directions for the LTSF task. We also advocate revisiting the validity of
Transformer-based solutions for other time series analysis tasks (e.g., anomaly
detection) in the future. Code is available at:
https://github.com/cure-lab/LTSF-Linear.

通过简单的线性模型实验发现在长期时间序列预测任务中，线性模型 LTSF-Linear 的效果优于复杂的基于 Transformer 方法，这引发人们对该任务以及其他时间序列分析任务中基于 Transformer 方法的有效性的反思。