Existing data-driven approaches in modeling and predicting time series data include ARIMA (Autoregressive Integrated Moving Average), Transformer-based models, LSTM (Long Short-Term Memory) and TCN (Temporal Convolutional Network). These approaches, and in particular deep learning-based models such as LSTM and TCN, have shown great results in predicting time series data. With the advancement of leveraging pre-trained foundation models such as Large Language Models (LLMs) and more notably Google's recent foundation model for time series data, {\it TimesFM} (Time Series Foundation Model), it is of interest to investigate whether these foundation models have the capability of outperforming existing modeling approaches in analyzing and predicting time series data. This paper investigates the performance of using LLM models for time series data prediction. We investigate the in-context learning methodology in the training of LLM models that are specific to the underlying application domain. More specifically, the paper explores training LLMs through in-context, zero-shot and few-shot learning and forecasting time series data with OpenAI {\tt o4-mini} and Gemini 2.5 Flash Lite, as well as the recent Google's Transformer-based TimesFM, a time series-specific foundation model, along with two deep learning models, namely TCN and LSTM networks. The findings indicate that TimesFM has the best overall performance with the lowest RMSE value (0.3023) and the competitive inference time (266 seconds). Furthermore, OpenAI's o4-mini also exhibits a good performance based on Zero Shot learning. These findings highlight pre-trained time series foundation models as a promising direction for real-time forecasting, enabling accurate and scalable deployment with minimal model adaptation.

翻译：现有建模和预测时序数据的数据驱动方法包括ARIMA（自回归积分滑动平均模型）、基于Transformer的模型、LSTM（长短期记忆网络）和TCN（时序卷积网络）。这些方法，特别是基于深度学习的模型如LSTM和TCN，在时序数据预测中已展现出优异性能。随着利用预训练基础模型（如大语言模型）的进展，尤其是谷歌近期推出的时序数据基础模型TimesFM（时序基础模型），探究这些基础模型在分析和预测时序数据方面是否具备超越现有建模方法的能力具有重要意义。本文研究使用LLM模型进行时序数据预测的性能。我们探讨了针对特定应用领域训练LLM模型的上下文学习方法。具体而言，本文通过上下文学习、零样本学习和少样本学习，使用OpenAI o4-mini和Gemini 2.5 Flash Lite，以及谷歌近期基于Transformer的时序专用基础模型TimesFM，结合两种深度学习模型（TCN和LSTM网络），对时序数据进行训练和预测。研究结果表明，TimesFM具有最佳综合性能，其RMSE值最低（0.3023）且推理时间具有竞争力（266秒）。此外，OpenAI的o4-mini在零样本学习中也表现出良好性能。这些发现突显了预训练时序基础模型作为实时预测领域的 promising 方向，能够以最小的模型适配实现准确且可扩展的部署。