Chong Zhang

Yunjiao Hu, Guangqiang Lan, Chong Zhang

Both the mean square polynomial stability and exponential stability of $θ$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\leθ\le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.

Hua Tang, Chong Zhang, Mingyu Jin et al.

Large language models (LLMs) have been applied in many fields and have developed rapidly in recent years. As a classic machine learning task, time series forecasting has recently been boosted by LLMs. Recent works treat large language models as \emph{zero-shot} time series reasoners without further fine-tuning, which achieves remarkable performance. However, there are some unexplored research problems when applying LLMs for time series forecasting under the zero-shot setting. For instance, the LLMs' preferences for the input time series are less understood. In this paper, by comparing LLMs with traditional time series forecasting models, we observe many interesting properties of LLMs in the context of time series forecasting. First, our study shows that LLMs perform well in predicting time series with clear patterns and trends, but face challenges with datasets lacking periodicity. This observation can be explained by the ability of LLMs to recognize the underlying period within datasets, which is supported by our experiments. In addition, the input strategy is investigated, and it is found that incorporating external knowledge and adopting natural language paraphrases substantially improve the predictive performance of LLMs for time series. Overall, our study contributes insight into LLMs' advantages and limitations in time series forecasting under different conditions.