Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing temporal patterns within the time series data. In this research, we study the statistical significance of the inclusion of geometric patterns in enhancing forecasting accuracy within the context of time series analysis. We introduce the Time-Geometric model, a combination of models designed to exploit both geometric and temporal patterns. The contribution of this research lies in advancing the domain of univariate time series prediction,as demonstrated through extensive empirical evaluations. Our findings underscore that leveraging geometric patterns, captured through Graph Neural Networks, yields statistically significant improvements in forecasting accuracy.

翻译：金融市场中的单变量时间序列预测是一项具有挑战性的任务。尽管已有大量统计模型与机器学习模型被提出用于应对这一挑战，但它们通常仅专注于分析时间序列数据中的时间模式。在本研究中，我们探讨了在时间序列分析背景下引入几何模式对提升预测精度的统计显著性。我们提出了时间-几何模型（Time-Geometric model），这是一个结合多种模型的设计，旨在同时利用几何模式与时间模式。本研究的贡献在于推动单变量时间序列预测领域的发展，这一结论通过广泛的实证评估得到了验证。我们的研究结果表明，通过图神经网络捕捉的几何模式能够显著提升预测精度，且具有统计显著性。