Title: Wavelet-SARIMA-Transformer: A Hybrid Model for Rainfall Forecasting Show Chinese title

Title: 小波-SARIMA-Transformer：一种降雨预测的混合模型

Abstract: This study develops and evaluates a novel hybridWavelet SARIMA Transformer, WST framework to forecast using monthly rainfall across five meteorological subdivisions of Northeast India over the 1971 to 2023 period. The approach employs the Maximal Overlap Discrete Wavelet Transform, MODWT with four wavelet families such as, Haar, Daubechies, Symlet, Coiflet etc. to achieve shift invariant, multiresolution decomposition of the rainfall series. Linear and seasonal components are modeled using Seasonal ARIMA, SARIMA, while nonlinear components are modeled by a Transformer network, and forecasts are reconstructed via inverse MODWT. Comprehensive validation using an 80 is to 20 train test split and multiple performance indices such as, RMSE, MAE, SMAPE, Willmotts d, Skill Score, Percent Bias, Explained Variance, and Legates McCabes E1 demonstrates the superiority of the Haar-based hybrid model, WHST. Across all subdivisions, WHST consistently achieved lower forecast errors, stronger agreement with observed rainfall, and unbiased predictions compared with stand alone SARIMA, stand-alone Transformer, and two-stage wavelet hybrids. Residual adequacy was confirmed through the Ljung Box test, while Taylor diagrams provided an integrated assessment of correlation, variance fidelity, and RMSE, further reinforcing the robustness of the proposed approach. The results highlight the effectiveness of integrating multiresolution signal decomposition with complementary linear and deep learning models for hydroclimatic forecasting. Beyond rainfall, the proposed WST framework offers a scalable methodology for forecasting complex environmental time series, with direct implications for flood risk management, water resources planning, and climate adaptation strategies in data-sparse and climate-sensitive regions. Show Chinese abstract

Abstract: 本研究开发并评估了一种新颖的混合小波SARIMA变换器，WST框架，以在1971年至2023年期间预测印度东北部五个气象分区的月度降雨量。该方法采用最大重叠离散小波变换，MODWT，使用四种小波族，如Haar、Daubechies、Symlet、Coiflet等，以实现降雨序列的平移不变、多分辨率分解。线性和季节性成分通过季节性ARIMA，SARIMA进行建模，而非线性成分通过变换器网络进行建模，预测结果通过逆MODWT重建。使用80比20的训练测试分割和多种性能指标，如RMSE、MAE、SMAPE、Willmotts d、技能得分、百分比偏差、解释方差和Legates McCabes E1进行全面验证，结果显示基于Haar的混合模型WHST具有优越性。在所有分区中，WHST始终表现出更低的预测误差，与观测降雨更强的一致性以及无偏预测，相比单独的SARIMA、单独的变换器和两阶段小波混合模型。通过Ljung Box检验确认了残差充分性，而泰勒图提供了相关性、方差保真度和RMSE的综合评估，进一步强化了所提出方法的稳健性。结果强调了将多分辨率信号分解与互补线性和深度学习模型相结合在水文气候预测中的有效性。除了降雨外，提出的WST框架为预测复杂环境时间序列提供了一种可扩展的方法，对数据稀疏和气候敏感地区的洪水风险管理、水资源规划和气候适应策略具有直接意义。