Time series data often contain initial transient periods before reaching a stable state, posing challenges in analysis and interpretation. In this paper, we propose a novel approach to detect and estimate the end of the initial transient in time series data. Our method leverages the reversal mean standard error (RMSE) as a metric for assessing the stability of the data. Additionally, we employ fractional filtering techniques to enhance the detection accuracy by filtering out noise and capturing essential features of the underlying dynamics. Combining with autocorrelation-corrected confidence intervals we provide a robust framework to automate transient detection and convergence assessment. The method ensures statistical rigor by accounting for autocorrelation effects, validated through simulations with varying time steps. Results demonstrate independence from numerical parameters (e.g., time step size, under-relaxation factors), offering a reliable tool for steady-state analysis. The framework is lightweight, generalizable, and mitigates inflated false positives in autocorrelated datasets.

翻译：时间序列数据在达到稳定状态前常包含初始瞬态阶段，这对分析与解释构成挑战。本文提出一种检测和估计时间序列数据中初始瞬态结束的新方法。该方法利用反向均值标准误差作为评估数据稳定性的度量指标。此外，我们采用分数滤波技术通过滤除噪声并捕捉底层动力学的基本特征来提高检测精度。结合自相关校正置信区间，我们提供了一个自动化瞬态检测与收敛性评估的稳健框架。该方法通过考虑自相关效应确保统计严谨性，并已通过不同时间步长的模拟验证。结果表明该方法独立于数值参数（如时间步长、欠松弛因子），为稳态分析提供了可靠工具。该框架具有轻量化、可推广性，并能有效降低自相关数据集中的虚警率。