摘要：

时间序列预测可广泛应用于工业生产、金融决策和灾害预警等领域。然而现有预测方法的研究对象大多是平稳时间序列，难以准确捕捉非平稳序列的演化特征。对于非平稳时间序列的预测方法也未能有效捕捉序列的多维特征，对序列动态感知不够完整，从而降低了预测的准确性。鉴于此，提出一种针对非平稳时间序列的预测机制。首先通过建模影响序列平稳性的季节性、局部趋势和长期趋势特征，提取非平稳时间序列的多维隐状态。然后结合前向后向算法与最大似然估计(MLE)计算最大转移概率，进而实现状态预测。由于该机制考虑了多种潜在非线性因素对非平稳序列的影响，且通过感知全局状态转移计算最大转移概率，从而提升了预测的准确性。最后通过方案级预测实例证实了所提机制的有效性。在9种不同领域的非平稳时间序列数据集上进行的消融实验结果验证了该机制各部分对于预测准确性的影响。对比实验结果表明，该机制的平均绝对百分比误差(MAPE)、均方根误差(RMSE)相比于多数预测方法更小，在金融领域的数据集上Legates-McCabe指数接近于1，是一种兼具鲁棒性和准确性的方法。

关键词: 特征提取, 状态转移链, 时间序列预测, 非平稳时间序列, 隐状态

Abstract:

Time series predicting is widely applicable in industrial production, financial decision-making, and early disaster warning. However, most existing methods primarily target stationary time series, failing to accurately capture the evolutionary characteristics of nonstationary sequences. Current approaches for nonstationary time series also inadequately extract multidimensional features and lack comprehensive dynamic perception, thereby compromising prediction accuracy. This study proposes a novel prediction mechanism for nonstationary time series to address these limitations. First, it models seasonality, local trends, and long-term trends that affect sequence stationarity to extract multidimensional hidden states. This study combines the forward—backward algorithm with Maximum Likelihood Estimation (MLE) to compute the maximum transition probabilities for state prediction. Because the mechanism incorporates multiple potential nonlinear factors influencing nonstationary sequences and calculating transition probabilities through a global state perception, it significantly improves the prediction accuracy. The effectiveness of the proposed mechanism is demonstrated through various case studies. Ablation experiments conducted on nine nonstationary time series datasets from diverse domains validate the contribution of each component to the overall prediction accuracy. Comparative results show that both the Mean Absolute Percentage Error (MAPE) and the Root Mean Square Error (RMSE) of the mechanism are consistently lower than those of baseline methods, with the Legates—McCabe index approaches 1 on financial datasets, thereby confirming its robustness and accuracy.

Key words: feature extraction, state transition chain, time series prediction, non-stationary time series, hidden state