Seasonal Decomposition Research Articles

STDNet: Spatio-Temporal Decompose Network for Predicting Arctic Sea Ice Concentration

In the context of global warming, the accurate prediction of Arctic Sea Ice Concentration (SIC) is crucial for the development of Arctic shipping routes. We have therefore constructed a lightweight, non-recursive spatio-temporal prediction model, the Spatio-Temporal Decomposition Network (STDNet), to predict the daily SIC in the Arctic. The model is based on the Seasonal and Trend decomposition using Loess (STL) decomposition idea to decompose the model into trend and seasonal components. In addition, we have designed the Global Sparse Attention Module (GSAM) to help the model extract global information. STDNet not only extracts seasonal signals and trend information with periodical correspondence from the data but also obtains the spatio-temporal dependence features in the data. The experimental methodology involves predicting the next 10 days based on the first 10 days of data. The prediction results provided the following metrics for the 10-day forecast of STDNet: Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and coefficient of determination of 1.988%, 3.541%, 5.843%, and 0.979, respectively. The average Binary Accuracy (BACC) at the beginning of September for the period 2018–2022 reached 93.85%. The proposed STDNet model outperforms and is lighter than existing deep-learning-based SIC prediction models.

Integrating spatial-temporal features into prediction tasks: A novel method for identifying the potential water pollution area in large river basins

Forecasting potential water pollution areas (PWPA) is essential for effective watershed management. However, there remains a limited understanding of the spatial-temporal features that influence water quality (WQ), and advanced technical methods for WQ forecasting. This study developed an integrated framework utilizing spatial-temporal graph convolution networks (STGCN) to enhance comprehension of the spatial-temporal features influencing WQ and to develop a practical module for integrating features into the WQ prediction. The Pearson correlation method and seasonal decomposition analysis described the WQ features. Subsequently, the spatial-temporal distribution of PWPA was assessed using both the comprehensive pollution index method and Cressman space interpolation technique. Data from 403 monitoring stations was collected from the Yangtze River basin (YZR), encompassing pollutants such as COD, TP and NH₄⁺-N. The finding revealed that maximum concentrations of COD (36.4 mg/L), TP (4.078 mg/L) and NH₄⁺-N (13.58 mg/L) exceeded the standard thresholds necessitating early warnings. A significant correlation among pollutants was observed with coefficients ranging from 0.356 to 0.475 (P < 0.001), indicating their potential utility in predicting PWPA. Seasonality components exhibited strong correlations with the original WQ (correlation coefficients ranging from 0.62 to 0.89), followed by residuals (from 0.37 to 0.61) and trend components (from 0.25 to 0.53). The geographic layout of WQ monitoring stations along river lines resembled a graph network structure, suggesting that watershed WQ prediction can be classified as a spatial-temporal prediction task. The STGCN model achieved R2 values ranging from 0.607 to 0.844 for each pollutant on the test datasets, surpassing traditional models such as RNN, LSTM, and GRU in predictive accuracy. PWPA occurrences were predominantly identified in the southwestern regions as well as within the middle and lower reaches of the YZR. These results validated that the developed framework is capable of forecasting PWPA in large-scale watersheds while supporting effective watershed management.

A hybrid wind power prediction model based on seasonal feature decomposition and enhanced feature extraction

Efficient and accurate wind power prediction is crucial for enhancing the reliability and safety of power system. The data-driven forecasting methods are regarded as an effective solution. However, the inherent randomness and nonlinearity of wind power systems, along with the abundance of redundant information in measurement data, present challenges to forecasting methods. The integration of precise and efficient techniques for data feature decomposition and extraction is essential in conjunction with advanced data-driven forecasting models. Focus on the seasonal variation characteristics of wind energy, a hybrid wind power prediction model based on seasonal feature decomposition and enhanced feature extraction is proposed. The effectiveness and superiority of the proposed method in predictive accuracy are demonstrated through comprehensive multi-model experiment comparisons.

Seasonal variation in suicide: age group and summer effects in the United States (2015–2020)

BackgroundSuicide is a global public health concern that affects more than 700,000 people globally every year. Seasonal variation in suicide rates is a phenomenon that has been well-documented, but recent data on the seasonality of suicide within specific age groups and sex in the United States remains less well understood.MethodsPublicly available data on monthly suicides was obtained from the Underlying Cause of Death database, CDC WONDER, from 2015–2020. The incidence of summer suicides, from June, July and August, for two groups, 15–24 and ages 25 + , was calculated and a two-sided test was performed. Seasonal Decomposition analysis was performed and time series created from 2015–2020 for every age group then converted into Trend, Seasonality, and Residual respectively.ResultsFor Americans ages 15–24, the highest spike in suicides was in autumn, September–October, with a trough in June. This is the only age group in which this occurred, differing from previous understanding of the seasonality of suicide in the literature. With all other age groups (25–34, 35–44, 45–54, 55–64, 65–74, 75 +) there was a consistent pattern of a peak in late spring/early summer, a small peak in fall, and a trough in late winter.ConclusionsThere is a seasonal variation in suicide deaths in the United States with the youngest group, ages 15–24, presenting a different pattern compared to other ages. There were no significant differences in suicide seasonality by sex.

Predicting multi-frequency crude oil price dynamics: Based on MIDAS and STL methods

Accurate prediction of crude oil prices is important for national energy security and socioeconomic development. Research on crude oil price forecasting has primarily focused on the overall price, overlooking the differentiated investment needs of different entities. To solve this problem, we introduce the Seasonal and Trend decomposition using Loess (STL) method into the Mixed Data Sampling (MIDAS) model. This enables us to more accurately analyze the predictive capability of predictors for crude oil prices at different frequencies. Selected predictors include the Dow Jones Index, US Dollar exchange rate, economic policy uncertainty, related crude oil and energy prices, carbon asset prices, and investor attention. Empirical results indicate that these predictors significantly enhance the forecasting accuracy across all components, with the strongest impact in the trend component. Interestingly, a lag effect is observed in the predictors' impact on the seasonal and residual components, but not on the trend component. Moreover, we calculate the duration of each predictor's effectiveness for different components of crude oil prices, distinguishing short-term and long-term effective predictors. This research offers novel insights into the design of crude oil price forecasting models, which is crucial for enhancing investor returns and maintaining stability in the energy market.

Deep Learning-Enabled De-Noising of Fiber Bragg Grating-Based Glucose Sensor: Improving Sensing Accuracy of Experimental Data

This paper outlines the successful utilization of deep learning (DL) techniques to elevate data quality for assessing Au-TFBG (tilted fiber Bragg grating) sensor performance. Our approach involves a well-structured DL-assisted framework integrating a hierarchical composite attention mechanism. In order to mitigate high variability in experimental data, we initially employ seasonal decomposition using moving averages (SDMA) statistical models to filter out redundant data points. Subsequently, sequential DL models extrapolate the normalized transmittance (Tn) vs. wavelength spectra, which showcases promising results through our SpecExLSTM model. Furthermore, we introduce the AttentiveSpecExLSTM model, integrating a composite attention mechanism to improve Tn sequence prediction accuracy. Evaluation metrics demonstrate its superior performance, including a root mean square error of 1.73 ± 0.05, a mean absolute error of 1.20 ± 0.04, and a symmetric mean absolute percentage error of 2.22 ± 0.05, among others. Additionally, our novel minima difference (Min. Dif.) metric achieves a value of 1.08 ± 0.46, quantifying wavelength for the global minima within the Tn sequence. The composite attention mechanism in the AttentiveSpecExLSTM adeptly captures both high-level and low-level dependencies, refining the model’s comprehension and guiding informed decisions. Hierarchical dot and additive attention within this model enable nuanced attention refinement across model layers; dot attention focuses on high-level dependencies, while additive attention fine-tunes its focus on low-level dependencies within the sequence. This innovative strategy enables accurate estimation of the spectral width (full-width half maxima) of the Tn curve, surpassing raw data’s capabilities. These findings significantly contribute to data quality enhancement and sensor performance analysis. Insights from this study hold promise for future sensor applications, enhancing sensitivity and accuracy by improving experimental data quality and sensor performance assessment.

An integrated approach for decomposing time series data into trend, cycle and seasonal components

ABSTRACT This study presents a methodology for decomposing time series data into trend, seasonal, and cyclical components using the moving linear model approach by Kyo and Kitagawa (Journal of Business Cycle Research, 19(3): 373-397, 2023). Our approach integrates seasonal adjustment and decomposition into a single framework. We evaluated our approach with two case studies: examining daily COVID-19 case data and the Index of Industrial Production (IIP) in Japan, comparing the results to seasonally adjusted IIP data. Performance metrics included the discrimination power index and the variance of the adjusted cyclical component. Our findings show that our method effectively extracts business cycle information, achieving higher discrimination power and greater adjusted variance compared to seasonally adjusted IIP data, highlighting the superior performance of our integrated seasonal adjustment method. We compared the proposed approach with a state-space modelling method by introducing an overall stability as a new indicator. The results demonstrated the stability of the estimations obtained with our proposed method.

Analysis of Google users' interests in information about pacifiers: an ecological digital study.

To determine the interests of Google users from different countries about pacifier-related information over time, through a quantitative and qualitative analysis. This infodemiology longitudinal retrospective ecological study investigated pacifier-related computational metadata from 22 countries using Google Trends platform. Initially, Relative Search Volume (RSV) time series data and their respective main queries were collected employing the topic "pacifier - subject" as the search strategy from January 2004 to June 2024, considering all categories. Data were then analyzed through seasonal decomposition to determine the trend, seasonal, and residual components of the collected time series using Python 3 programming libraries in a Google Collaboratory interface. Additionally, Mann-Kendall tests were performed to access the significance level of trends observed from the seasonal decomposition. Finally, the queries were qualitatively evaluated to identify the main subjects related to users' interests. Statistical significance was determined with p values < 0.05. In general, RSV time series curves exhibited upward trends in all analyzed countries over the years, with significance levels demonstrated by the Mann-Kendall tests. Moreover, queries often centered around types of pacifiers, encompassing searches specifically for certain commercial brands. Some searches concerning newborn and baby care were also observed, particularly highlighting breastfeeding practices. Google users have shown an increasing interest in pacifier-related topics. These data can help understand the needs and concerns of parents and caregivers regarding pacifier use, ultimately supporting the development of effective educational strategies.

Red Sea crisis impacts on maritime shipping networks

The Red Sea crisis (RSC) is an ongoing military conflict affecting maritime trade. Based on automatic identification system data, this study analyzed the changes in vessel behavior in the Red Sea using the seasonal decomposition method. The number and speed of vessels decreased significantly after the RSC, and many vessels chose to sail away from the Red Sea rather than anchor at its shores. Additionally, the impact of the RSC on maritime shipping networks was analyzed based on metrics in complex networks. Although shipping network structures were changed by the RSC, they still exhibited resilience. Finally, this study analyzed the RSC future impacts on maritime shipping networks based on node attacks and the Markov method. Because of their resilience, only ports in the top 20 % needed to be considered. This study provides valuable insights for maritime transportation authorities to formulate port strategies and route layouts in response to the RSC.

Spatial-temporal analysis and trend prediction of regional crop disease based on electronic medical records

Intelligent diagnosis of individual crop diseases has matured. How to understand the evolution patterns and predict regional disease trends remains a significant challenge. Plant Electronic Medical Records (PEMRs) offer valuable spatial-temporal characteristics about crop diseases, presenting a new opportunity for predicting the occurrence of regional diseases. In this study, we used a large prescription database from Beijing (2018–2021) to reframe regional disease prediction as a time series forecasting task. Firstly, to analyze spatial-temporal evolution patterns, we use ArcGIS to extract key information and identify potential connections between different disease occurrence points. Then, we developed a novel deep learning combined model SV-CBA, which combines Seasonal and Trend decomposition (STL) with Variational Mode Decomposition (VMD) to identify trend, seasonal, and residual components, and re-decomposes the residuals. STL-VMD can capture long-term trends and periodic variations while managing nonlinear and volatile characteristics. The CNN-BiLSTM-Attention model calculates disease trends by linearly integrating predictions of each sub-series. To reduce computational complexity while maintaining predictive performance, we propose an improved simplified attention mechanism. Our model demonstrates superior performance in both comparative and ablation experiments using the PEMRs dataset, outperforming numerous other models. This study provides accurate disease trend predictions, aiding farmers and regional managers in agricultural production management.

Full-scale wind turbine performance assessment using the turbine performance integral (TPI) method: a study of aerodynamic degradation and operational influences

Abstract. This study investigates how blade aerodynamic modifications, including leading edge roughness (LER), influence wind turbine performance over their operational lifespan. It introduces a methodology developed to examine the intricate relationship between blade erosion, blade enhancements, operations and maintenance (O&amp;amp;M) events, control programmable logic controller (PLC) parameter updates, and their cumulative impact on turbine efficiency. Analysing data from 12 multi-megawatt offshore turbines over a 12-year period, the investigation hinges on the integration of supervisory control and data acquisition (SCADA) data, O&amp;amp;M records, and air density corrections. A key contribution is the development of the turbine performance integral (TPI) method, which, for the investigated turbines, leverages generator speed and power output data to track performance trajectories. Seasonal trend decomposition using locally estimated scatterplot smoothing (STL) further isolates long-term trends and seasonal variations in performance. Despite data availability and quality limitations, the study reveals significant findings concerning the impact of manufacturer software updates on turbine control strategies, resulting in improved performance; the variable effects of blade repairs and enhancements; and the complex interaction between O&amp;amp;M events and performance. This work applies a methodical approach and statistical rigour, offering a path forward for effectively monitoring wind turbine efficiency and advancing renewable energy.

Forecasting oil futures markets using machine learning and seasonal trend decomposition

ABSTRACT Can machine learning improve prediction for seasonal commodity prices? We explore the effectiveness of a combined method that integrates seasonal trend decomposition using LOESS (STL) with machine learning (ML), referred to as STL-ML. We apply Extreme Gradient Boosting and Random Forest to forecast oil futures price dynamics over a sample period from 2004 to 2023. Our STL-ML results indicate no significant improvement for crude oil futures but enhanced accuracy for heating oil futures, highlighting STL’s benefit for datasets with strong seasonality. We demonstrate the potential for machine learning performance enhancement with STL, emphasising the variability of predictive model effectiveness due to data characteristics and providing insights for refining investment strategies based on seasonality and trends.

About Air Quality Assessment using Time Series Analysis Techniques on Air Particles Data

This study investigates the dynamics of air pollution caused by particulate matter (PM10 and PM2.5) in Omsk, Russia. Data collected from the Sensor.Community network between 2021 and 2023 were analyzed using time series analysis methods. The findings reveal a subtle weekly seasonality in the data, potentially attributed to fluctuations in industrial activity and traffic patterns throughout the week. Additionally, a concerning trend of deteriorating air quality was identified, characterized by increasing annual average concentrations of PM10 and PM2.5. The study employed various time series analysis techniques, including Empirical Cumulative Distribution Function (ECDF), Seasonal and Trend decomposition using Loess (STL), and autocorrelation function (ACF) analysis. These methods allowed for the visualization and examination of data distribution, trend identification, and seasonality detection. Furthermore, the Mann-Kendall test confirmed a statistically significant trend of increasing pollution levels over the three-year period. To enhance the accuracy of spatial analysis, data interpolation was performed using kriging with a Gaussian model. This method, compared to simple interpolation, provides a more precise assessment of the spatial distribution of pollutants. The study also implemented Long Short-Term Memory (LSTM) for forecasting hourly pollution values. LSTM exhibited promising results, demonstrating its potential for developing early warning systems, particularly when combined with meteorological data such as wind forecasts. The results highlight the need for effective measures to mitigate air pollution in Omsk and emphasize the importance of utilizing data from diverse sources, including official air quality monitoring stations, to ensure accuracy and reliability in air quality assessments.

Assessing long-term water storage dynamics in Afghanistan: An integrated approach using machine learning, hydrological models, and remote sensing

Assessment of Terrestrial Water Storage (TWS) components is crucial for understanding regional climate and water resources, particularly in arid and semi-arid regions like Afghanistan. Given the scarcity of ground-based data, this study leverages remote sensing datasets to quantify water storage changes. We integrated Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-on (GRACE-FO) data with WaterGap, Global Land Water Storage (GWLS), Catchment Land Surface Model (CLSM), and climate variables (precipitation, temperature, potential evapotranspiration) using artificial neural networks (ANN) and random forests (RF). Additionally, Ice, Cloud, and Land Elevation Satellite (ICESat-1,2) data were utilized to estimate glacier mass changes. Seasonal trend decomposition using Loess (STL) was applied to assess TWS changes from 2003 to 2022. Our methodology reveals a high correlation (R = 0.90–0.97) between reconstructed and observed TWS anomalies across Afghanistan's major basins. Glacier mass decreased by −0.59 and −1.17 Gt/year during 2003–2009 and 2018–2022, respectively, while overall TWS declined by −2.46 Gt/year. The HRB experienced the largest TWS loss (−1.47 Gt/year), primarily due to groundwater depletion (−1.18 Gt/year). These findings underscore the importance of our approach for assessing water resources, providing vital insights for sustainable management under a changing climate in a data-scarce country.

What drives the distinct evolution of the Aral Sea and Lake Balkhash? Insights from a novel CD-RF-FA method

Study RegionThe Aral Sea and Lake Balkhash. Study FocusThis study explores the impacts of climate change and human activities on the inflow of the Aral Sea and Lake Balkhash, revealing the different driving factors behind the evolution of inland lakes in arid environments. To achieve this, we propose a novel approach that combines classical seasonal decomposition with Random Forest and Factor Analysis (CD-RF-FA) to quantitatively assess the influences of climate change and human activities on lake inflow. New Hydrological Insights for the RegionDuring the period from 1960 to 1990, anthropogenic factors predominantly influenced the inflow to the lakes, contributing 89.9 %, 91.8 %, and 91.6 % to the Lake Balkhash Basin (BAK), the Syr Darya Basin (SYR), and the Amu Darya Basin (AMU), respectively. However, from 1991 to 2020, the influence of human activities diminished, and climate variables gradually dominated the changes in inflow, contributing 52.2 % and 47.2 % to BAK and SYR, respectively, with upstream inflow being the main driving factor. Additionally, reservoir construction and political factors also played significant roles in the variation of inflow, exerting direct or indirect effects. This study provides crucial insights into the complex interplay of factors affecting inland lakes in arid regions and informs strategies to mitigate the Aral Sea Syndrome.

An epidemiological and spatiotemporal analysis of visceral leishmaniasis in West Pokot, Kenya, between 2018 and 2022

BackgroundVisceral leishmaniasis (VL) remains a significant public health concern in West Pokot County, Kenya, where a large outbreak between 2020 and 2022 emphasised the need for improved VL control strategies. However, these measures are partially hampered by limited insight into the geographical distribution of cases and localised outbreaks of the disease. This study aimed to describe the epidemiology and spatiotemporal patterns of VL in West Pokot between 2018 and 2022, in order to map the spread of VL transmission and identify regions that should be prioritised for control interventions.MethodsVL patient demographics and village of residence were retrieved from admission records of Kacheliba Sub-County Hospital in West Pokot, Kenya. The temporal trend in VL admissions between 2018 and 2022 was analysed using seasonal decomposition analysis. To describe the spatial distribution of VL cases, geographic coordinates of villages of residence were collected from pre-established databases, and VL incidence was mapped at the sub-location level. Hotspot analysis was performed per study year to identify villages with high VL incidence, and scan statistics were applied to detect spatiotemporal clusters of VL cases during the study period.ResultsA total of 1948 VL patients were reported between 2018 and 2022. The annual number of cases increased from 245 in 2019 to 598 in 2022, and VL admissions were generally higher at the start of the wet seasons. 70% of the VL cases could be georeferenced, and mapping of VL incidence revealed high case rates in the east of West Pokot during the complete study period. The eastern villages Lotongot and Chepaywat were marked as VL hotspots at a 99% confidence level in all study years. In addition, five significant spatiotemporal clusters were detected in the east and north, suggestive of local VL outbreaks in these regions.ConclusionsThe increase in VL hospital admissions during the study period stresses the need for enhanced VL control and outbreak mitigation in West Pokot. These control measures should be focused on the hotspot regions in the east of the county.

How environmental data enables intelligent navigation: Factors assessment of affecting the navigation in the Northeast Arctic Route

Due to the more favorable navigational environment and higher safety along Northeast Arctic Route, this route is being used more and more frequently for international shipping. In this research, the factor analysis method is applied to assess the navigational environment of each sea area in the Northeast Arctic Route, revealing the effects of Arctic navigation influence factor on the navigational environment, and analyzing the change trend of the navigational environment of different sea areas in different seasons. Further, the effects of multiple factors on the number of voyages are discussed through multiple stepwise regression model, including the navigational environment score, geopolitical risk, export & import trade and the probability of pollution accidents, then the Interrupted time series analysis (ITSA) method combined with seasonal decomposition is explored the effect of emergencies on the number of voyages on the Northeast Arctic Route. The number of voyages on the Northeast Arctic Route has been altered to varying degrees by the occurrence of various emergencies. Further, the Yamal LNG project and the Russian-Ukrainian conflict have a significant effect on the number of voyages, while the Covid-19 epidemic has a lesser effect on the number of voyages.

Temporal distribution characteristics of hand, foot and mouth disease in Beijing, 2008-2023

Objective: To analyze the temporal distribution characteristics of hand, foot and mouth disease (HFMD) in Beijing and provide reference evidence in HFMD prevention and control. Methods: The monthly incidence data of HFMD in Beijing from 2008 to 2023 were collected from Notifiable Disease Management Information System of the Chinese Information System of Disease Control and Prevention, and the epidemiological characteristics of HFMD were analyzed by the methods of time series seasonal decomposition graph, concentration degree, and circular distribution.The WPS office software 2019 was used to clean the data, Python software 3.12 was used to analyze and make statistical charts. Results: The monthly incidence fluctuation of HFMD in Beijing from 2008 to 2015 was higher than that from 2016 to 2022. From 2016 to 2022, the fluctuation range of monthly incidence showed a gradually decreasing trend.From 2008 to 2015, the concentration (M) was 0.58, indicating a relatively strong seasonality; the mean angle (α) calculated by the circular distribution method was 174.95°, and the mean angle standard deviation (s) was 60.43°. The annual incidence peak occurred on June 27, and the incidence peak period was from April 27 to August 27. From 2016 to 2019 and 2023, the M was 0.57, indicating a relatively strong seasonality. The α was 228.05°, and s was 61.44°. The annual incidence peak occurred on August 20, and the incidence peak period was from June 18 to October 21. From 2020 to 2022, the M was 0.42, indicating a seasonality, the α was 238.27° and s was 76.35°. The annual incidence peak occurred on July 15, and the incidence peak period was from June 14 to November 14. The α of 2008-2015, 2016-2019 and 2023, and 2020-2022 were tested by the Watson-Williams method and the difference was statistically significant (F=33 443.09, P<0.001). In 2023, the M was 0.77, indicating a strong seasonality. The incidence peak occurred on September 16, and the incidence peak period was from August 5 to October 28. Conclusions: The seasonality of HFMD in Beijing was obvious from 2008 to 2023, and the incidence peak day and peak period overall had rearward shifts. It is necessary to strengthen the comprehensive analysis of the distribution characteristics at different dimensions and the comprehensive prevention and control in key areas, places, and populations during the peak incidence period.

Optimizing Retail Inventory Management Through Time Series Analysis

The purpose of this study is to investigate the application of time series analysis in the management of retail inventory, with a particular emphasis on the precision of forecasting as well as the applicability of ARIMA models and seasonal decomposition techniques. This study aimed to evaluate these models' effectiveness in improving the scientific and precise nature of inventory management. This was accomplished by using legitimate retail data. According to the findings, the ARIMA model is effective in managing data that is stable or does not exhibit seasonal patterns. On the other hand, the seasonal decomposition technique demonstrates strong forecasting accuracy in managing data that exhibits seasonal fluctuations. Not only does this research improve the theoretical implementation of time series analysis in the retail sector, but it also provides retailers with practical strategies for mitigating economic losses that are caused by inventory imbalance. When it comes to the management of retail inventory, the findings of the research are significant for improving both overall cost control and customer satisfaction.

SMGformer: integrating STL and multi-head self-attention in deep learning model for multi-step runoff forecasting

Accurate runoff forecasting is of great significance for water resource allocation flood control and disaster reduction. However, due to the inherent strong randomness of runoff sequences, this task faces significant challenges. To address this challenge, this study proposes a new SMGformer runoff forecast model. The model integrates Seasonal and Trend decomposition using Loess (STL), Informer’s Encoder layer, Bidirectional Gated Recurrent Unit (BiGRU), and Multi-head self-attention (MHSA). Firstly, in response to the nonlinear and non-stationary characteristics of the runoff sequence, the STL decomposition is used to extract the runoff sequence’s trend, period, and residual terms, and a multi-feature set based on ‘sequence-sequence’ is constructed as the input of the model, providing a foundation for subsequent models to capture the evolution of runoff. The key features of the input set are then captured using the Informer’s Encoder layer. Next, the BiGRU layer is used to learn the temporal information of these features. To further optimize the output of the BiGRU layer, the MHSA mechanism is introduced to emphasize the impact of important information. Finally, accurate runoff forecasting is achieved by transforming the output of the MHSA layer through the Fully connected layer. To verify the effectiveness of the proposed model, monthly runoff data from two hydrological stations in China are selected, and eight models are constructed to compare the performance of the proposed model. The results show that compared with the Informer model, the 1th step MAE of the SMGformer model decreases by 42.2% and 36.6%, respectively; RMSE decreases by 37.9% and 43.6% respectively; NSE increases from 0.936 to 0.975 and from 0.487 to 0.837, respectively. In addition, the KGE of the SMGformer model at the 3th step are 0.960 and 0.805, both of which can maintain above 0.8. Therefore, the model can accurately capture key information in the monthly runoff sequence and extend the effective forecast period of the model.