STL Decomposition Research Articles

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.

Research on time characteristic sea surface temperature prediction based on decomposition

Abstract The effective prediction of sea surface temperature has become a hot topic of scientific research. The hidden characteristics and time characteristics of sea surface temperature are studied, and a new sea surface temperature prediction model SLA based on decomposition is proposed in this paper. Firstly, the trend term and periodic seasonal term of sea surface temperature were decomposed by STL decomposition algorithm, which improved the problem of single characteristics of sea surface. Secondly, on the basis of the calculation method of the improved LSTM model and the attention mechanism, the problem that the prediction of sea surface temperature cannot be remembered in the long term and the influence weight of historical information is ignored is solved. Finally, the sea surface temperature of the South China Sea (112.125E,10.125N) was taken as the research object, and the experimental verification was carried out in three data sets. The experimental results show that the SLA model proposed in this paper has good prediction accuracy.

STL decomposition analysis for anomaly detection in soil radon and thoron concentrations along Chite fault in Aizawl

STL decomposition analysis for anomaly detection in soil radon and thoron concentrations along Chite fault in Aizawl

Deformation prediction of arch dams by coupling STL decomposition and LSTM neural network

Deformation prediction of arch dams by coupling STL decomposition and LSTM neural network

STSB Model Based on STL Decomposition Algorithm and Its Application in Stock Price Prediction Studies

STSB Model Based on STL Decomposition Algorithm and Its Application in Stock Price Prediction Studies

An ensemble model for accurate prediction of key water quality parameters in river based on deep learning methods

Deep learning models provide a more powerful method for accurate and stable prediction of water quality in rivers, which is crucial for the intelligent management and control of the water environment. To increase the accuracy of predicting the water quality parameters and learn more about the impact of complex spatial information based on deep learning models, this study proposes two ensemble models TNX (with temporal attention) and STNX (with spatio-temporal attention) based on seasonal and trend decomposition (STL) method to predict water quality using geo-sensory time series data. Dissolved oxygen, total phosphorus, and ammonia nitrogen were predicted in short-step (1 h, and 2 h) and long-step (12 h, and 24 h) with seven water quality monitoring sites in a river. The ensemble model TNX improved the performance by 2.1%–6.1% and 4.3%–22.0% relative to the best baseline deep learning model for the short-step and long-step water quality prediction, and it can capture the variation pattern of water quality parameters by only predicting the trend component of raw data after STL decomposition. The STNX model, with spatio-temporal attention, obtained 0.5%–2.4% and 2.3%–5.7% higher performance compared to the TNX model for the short-step and long-step water quality prediction, and such improvement was more effective in mitigating the prediction shift patterns of long-step prediction. Moreover, the model interpretation results consistently demonstrated positive relationship patterns across all monitoring sites. However, the significance of seven specific monitoring sites diminished as the distance between the predicted and input monitoring sites increased. This study provides an ensemble modeling approach based on STL decomposition for improving short-step and long-step prediction of river water quality parameter, and understands the impact of complex spatial information on deep learning model.

Analyzing variation of water inflow to inland lakes under climate change: Integrating deep learning and time series data mining

The alarming depletion of global inland lakes in recent decades makes it essential to predict water inflow from rivers to lakes (WIRL) trend and unveil the dominant influencing driver, particularly in the context of climate change. The raw time series data contains multiple components (i.e., long-term trend, seasonal periodicity, and random noise), which makes it challenging for traditional machine/deep learning techniques to effectively capture long-term trend information. In this study, a novel FactorConvSTLnet (FCS) method is developed through integrating STL decomposition, convolutional neural networks (CNN), and factorial analysis into a general framework. FCS is more robust in long-term WIRL trend prediction through separating trend information as a modeling predictor, as well as unveiling predominant drivers. FCS is applied to typical inland lakes (the Aral Sea and the Lake Balkhash) in Central Asia, and results indicate that FCS (Nash-Sutcliffe efficiency = 0.88, root mean squared error = 67m³/s, mean relative error = 10%) outperforms the traditional CNN. Some main findings are: (i) during 1960–1990, reservoir water storage (WSR) was the dominant driver for the two lakes, respectively contributing to 71% and 49%; during 1991–2014 and 2015–2099, evaporation (EVAP) would be the dominant driver, with the contribution of 30% and 47%; (ii) climate change would shift the dominant driver from human activities to natural factors, where EVAP and surface snow amount (SNW) have an increasing influence on WIRL; (iii) compared to SSP1-2.6, the SNW contribution would decrease by 26% under SSP5-8.5, while the EVAP contribution would increase by 9%. The findings reveal the main drivers of shrinkage of the inland lakes and provide the scientific basis for promoting regional ecological sustainability.

Monthly electricity generation forecast based on similar month screening and STL decomposition

In order to solve the problems of monthly electricity generation forecasting being limited by the lack of actual data source, and the large errors caused by the influence of various factors such as weather and holidays, and the limitations of the applicable scenarios of the existing research results, a monthly electricity generation forecasting model based on similar month screening and Seasonal and Trend decomposition using Loess (STL) was proposed in this paper. The complementary advantages of Multiple Linear Regression (MLR) and Improved Random Forest Regression (RFR) are utilized to achieve the monthly electricity generation prediction in the province. This prediction model does not require a large number of data to obtain a better prediction accuracy, and breaks through the limitations of the existing monthly electricity prediction model that are only suitable for a certain industry or a certain region. Experiments performed on an actual electric power generation series validate the efficiency of the proposed model.

Optimizing Metro Passenger Flow Prediction: Integrating Machine Learning and Time-Series Analysis with Multimodal Data Fusion

Accurate passenger flow forecasting is crucial in urban areas with growing transit demand. In this paper, we propose a method that combines advanced machine learning with rigorous time series analysis to improve prediction accuracy by integrating different datasets, providing a prescriptive example for passenger flow prediction in urban rail transit systems. The study employs advanced machine learning algorithms and proposes a novel prediction model that combines two-stage decomposition (seasonal and trend decomposition using LOESS–ensemble empirical mode decomposition (STL-EEMD)) and gated recurrent units. First, the STL decomposition algorithm is applied to break down the preprocessed data into trend terms, periodic terms, and irregular fluctuation terms. Then, the EEMD decomposition algorithm is employed to further decompose the irregular fluctuation terms, yielding multiple IMF components and residual residuals. Subsequently, the decomposed data from STL and EEMD are partitioned into training and test sets and normalized. The training set is utilized to train the model for optimal performance in predicting subway short-time passenger flow. The synthesis of these sophisticated methodologies serves to substantially enhance both the predictive precision and the broad applicability of the forecasting models. The efficacy of the proposed approach is rigorously evaluated through its application to empirical metro passenger flow datasets from diverse urban centers, demonstrating marked superiority in predictive performance over traditional forecasting methods. The insights gleaned from this study bear significant ramifications for the strategic planning and administration of public transportation infrastructures, potentially leading to more strategic resource allocation and an enhanced commuter experience.

Meta-Learning Enhanced Trade Forecasting: A Neural Framework Leveraging Efficient Multicommodity STL Decomposition

In the dynamic global trade environment, accurately predicting trade values of diverse commodities is challenged by unpredictable economic and political changes. This study introduces the Meta-TFSTL framework, an innovative neural model that integrates Meta-Learning Enhanced Trade Forecasting with efficient multicommodity STL decomposition to adeptly navigate the complexities of forecasting. Our approach begins with STL decomposition to partition trade value sequences into seasonal, trend, and residual elements, identifying a potential 10-month economic cycle through the Ljung–Box test. The model employs a dual-channel spatiotemporal encoder for processing these components, ensuring a comprehensive grasp of temporal correlations. By constructing spatial and temporal graphs leveraging correlation matrices and graph embeddings and introducing fused attention and multitasking strategies at the decoding phase, Meta-TFSTL surpasses benchmark models in performance. Additionally, integrating meta-learning and fine-tuning techniques enhances shared knowledge across import and export trade predictions. Ultimately, our research significantly advances the precision and efficiency of trade forecasting in a volatile global economic scenario.

Comparison of SARIMA, Bagging Exponential Smoothing with STL Decomposition and Robust STL Decomposition for Forecasting Red Chili Production

Time series analysis enables the identification of trends and patterns in data, allowing for the development of forecasting models that predict future values. One effective approach for forecasting seasonal time series data is the Seasonal Autoregressive Integrated Moving Average (SARIMA) method. Bagging Exponential Smoothing with STL Decomposition (BES-STL) is an ensemble machine learning method aimed at enhancing forecasting accuracy. STL Method, which stands for Seasonal-Trend decomposition using Loess, is utilized to decompose time series data into three components, namely trend, seasonal, and remainder components. In the remainder component, the process of bootstrap aggregation (bagging) with Moving Block Bootstrapping (MBB) is used to obtain synthetic data, followed by averaging the value by month from the entire series as the forecast results. A comparative analysis was conducted using the SARIMA, BES-STL, and BES-RSTL models. The optimal model, with the lowest MAPE and RMSE, is then implemented to predict national red chili production. The results indicate that the SARIMA(1,1,1)(0,1,1)12 model has the best performance with a MAPE of 7.06 and a RMSE of 95,473. The top-performing model is utilized to forecast data from January to December 2022. Additionally, the forecasted results are compared to the actual data, resulting in a highly precise MAPE of 5.39.

Spatiotemporal analysis and forecasting of lumpy skin disease outbreaks in Ethiopia based on retrospective outbreak reports.

Lumpy skin disease is a viral disease that affects cattle belonging to genus Capripoxvirus (Poxviridae) and lead to significant economic losses. The objective of this study was to evaluate the distribution of lumpy skin disease (LSD) outbreaks and predict future patterns based on retrospective outbreak reports in Ethiopia. Data were collected through direct communication with regional laboratories and a hierarchical reporting system from the Peasant Associations to Ministry of Agriculture. Time-series data for the LSD outbreaks were analyzed using classical additive time-series decomposition and STL decomposition. Four models (ARIMA, SARIMA, ETS, STLF) were also used to forecast the number of LSD outbreaks that occurred each month for the years (2021-2025) after the models' accuracy test was performed. Additionally, the space-time permutation model (STP) were also used to study retrospective space-time cluster analysis of LSD outbreaks in Ethiopia. This study examined the geographical and temporal distribution of LSD outbreaks in Ethiopia from 2008 to 2020, reporting a total of 3,256 LSD outbreaks, 14,754 LSD-positive cases, 7,758 deaths, and 289 slaughters. It also covered approximately 68% of Ethiopia's districts, with Oromia reporting the highest LSD outbreaks. In the LSD's temporal distribution, the highest peak was reported following the rainy season in September to December and its lowest peak in the dry months of April and May. Out of the four models tested for forecasting, the SARIMA (3, 0, 0) (2, 1, 0) [12] model performed well for the validation data, while the STLF+Random Walk had a robust prediction for the training data. Thus, the SARIMA and STLF+Random Walk models produced a more accurate forecast of LSD outbreaks between 2020 and 2025. From retrospective Space-Time Cluster Analysis of LSD, eight possible clusters were also identified, with five of them located in central part of Ethiopia. The study's time series and ST-cluster analysis of LSD outbreak data provide valuable insights into the spatial and temporal dynamics of the disease in Ethiopia. These insights can aid in the development of effective strategies to control and prevent the spread of the disease and holds great potential for improving efforts to combat LSD in the country.

A hybrid model based on STL with simple exponential smoothing and ARMA for wind forecast in a Brazilian nuclear power plant site

In the event of a nuclear accident with release of radioactive effluents into the environment, the Environmental Control System (ECS) at the Central Nuclear Almirante Álvaro Alberto (CNAAA) nuclear complex estimates the movement of the radioactive plume produced and provides forecast for one and two hours ahead. The prediction is based on the current accident and atmospheric data collected from meteorological stations spread across the site. In this way, the ECS estimates the spatial dose and dose rates distribution at ground level. The one- and two-hour forecast made by the ECS use the naïve method, which repeats the last known value. Its results are satisfactory if the next value to be collected does not differ substantially from the last known value. However, observing real data, acquired in loco, this fact does not occur in practice, which can make the forecast considerably erroneous.The purpose of this work is to investigate new approaches to improve ECS forecasting method, making it more accurate in real situations. To this end, the Seasonal and Trend decomposition using Loess (STL) was used together with the Simple Exponential Smoothing (SES) method and the Autoregressive Moving Average (ARMA) model to forecast weather parameters at the Angra site. The STL method was chosen since it has a robust mathematical decomposition method, capable of satisfactorily dealing with time series that have a high frequency of acquisition, the so-called intraday series. This model uses the Loess method, which is a smoothing technique based on locally adjusted regressions. The SES method and ARMA model are the techniques that most adequately fit the trend and remainder components generated by the STL decomposition, respectively. In the scope of this work, the method is applied to forecast wind speed measurements made at one of the meteorological towers used by the ECS. Using the hybrid model developed, an increase the of 101.39% in the Mean Absolute Percentage Error (MAPE), was achieved when compared to the ECS forecast method.

Forecasting performance of machine learning, time series, and hybrid methods for low‐ and high‐frequency time series

One of the main objectives of the time series analysis is forecasting, so both Machine Learning methods and statistical methods have been proposed in the literature. In this study, we compare the forecasting performance of some of these approaches. In addition to traditional forecasting methods, which are the Naive and Seasonal Naive Methods, S/ARIMA, Exponential Smoothing, TBATS, Bayesian Exponential Smoothing Models with Trend Modifications and STL Decomposition, the forecasts are also obtained using seven different machine learning methods, which are Random Forest, Support Vector Regression, XGBoosting, BNN, RNN, LSTM, and FFNN, and the hybridization of both statistical time series and machine learning methods. The data set is selected proportionally from various time domains in M4 Competition data set. Thereby, we aim to create a forecasting guide by considering different preprocessing approaches, methods, and data sets having various time domains. After the experiment, the performance and impact of all methods are discussed. Therefore, most of the best models are mainly selected from machine learning methods for forecasting. Moreover, the forecasting performance of the model is affected by both the time frequency and forecast horizon. Lastly, the study suggests that the hybrid approach is not always the best model for forecasting. Hence, this study provides guidelines to understand which method will perform better at different time series frequencies.

Does climate risk matter for gold price volatility?

This study utilizes predictive modelling and STL decomposition to revisit the potential driving effect of climate risk on gold price volatility and observes the utility benefits of this risk. We find that gold price volatility is negatively correlated with physical risk (El Niño). Moreover, the parameter estimation results provide evidence for the heterogeneous influence of SOI on gold price volatility. Moreover, we find evidence for the presence of the physical risk of climate change on the prediction of gold price volatility, where the extended model incorporating the seasonal component of SOI has a better prediction.

El Niño Index Prediction Based on Deep Learning with STL Decomposition

ENSO is an important climate phenomenon that often causes widespread climate anomalies and triggers various meteorological disasters. Accurately predicting the ENSO variation trend is of great significance for global ecosystems and socio-economic aspects. In scientific practice, researchers predominantly employ associated indices, such as Niño 3.4, to quantitatively characterize the onset, intensity, duration, and type of ENSO events. In this study, we propose the STL-TCN model, which combines seasonal-trend decomposition using locally weighted scatterplot smoothing (LOESS) (STL) and temporal convolutional networks (TCN). This method uses STL to decompose the original time series into trend, seasonal, and residual components. Each subsequence is then individually predicted by different TCN models for multi-step forecasting, and the predictions from all models are combined to obtain the final result. During the verification period from 1992 to 2022, the STL-TCN model effectively captures index features and improves the accuracy of multi-step forecasting. In historical event simulation experiments, the model demonstrates advantages in capturing the trend and peak intensity of ENSO events.

An analysis on the spatiotemporal behavior of inbound tourists in Jiaodong Peninsula based on Flickr geotagged photos

Exploring the spatiotemporal behavior characteristics of inbound tourists is of great practical significance to the management and planning of attractions. Based on Flickr geotagged photos and metadata, the research analyzes the spatiotemporal behavior characteristics of inbound tourists in Jiaodong Peninsula from the perspective of tourist flow network. We decompose the time series characteristics of tourists with STL decomposition algorithm, and predict the inbound tourism trend through the time series model. We propose the Hot Status Index (HSI) based on network centrality, extract and analyze the distribution pattern of inbound tourism hotspots with the structural hole method. The k-core decomposition algorithm is introduced to analyze the hierarchical characteristics of the tourist flow network. And Fast Unfolding algorithm is adopted to analyze the characteristics of community aggregation under different scales, dividing the scenic area into four communities. The results show that the time series model can accurately estimate the trend of the number of tourists. And there is a “competition” effect among attractions in Jiaodong Peninsula. The attractions show a hierarchy effect, of which the core layer has obvious small-world characteristics, with a clustering coefficient of 0.768. The inter-city tourist flow in Jiaodong Peninsula reveals a closed “multi-triangle” distribution pattern, mainly in the marginal coastal cities. Qingdao old town presents community stability, and other urban communities have a scale effect, mainly comprising two tourism circles.

How the real estate indexes have performed during the COVID-19 crisis? Multifractal analysis revisited with wavelet

PurposeThe purpose of this paper is to test the existence of stylized facts, such as the volatility clustering, heavy tails seen on financial series, long-term dependence and multifractality on the returns of four real estate indexes using different types of indexes: conventional and Islamic by comparing pre and during COVID-19 pandemic.Design/methodology/approachFirstly, the authors examined the characteristics of the indexes. Secondly, the authors estimated the parameters of the stable distribution. Then, the long memory is detected via the estimation of the Hurst exponents. Afterwards, the authors determine the graphs of the multifractal detrended fluctuation analysis (MF-DFA). Finally, the authors apply the WTMM method.FindingsThe results suggest that the real estate indexes are far from being efficient and that the lowest level of multifractality was observed for Islamic indexes.Research limitations/implicationsThe inefficiency behavior of real estate indexes gives us an idea about the prediction of the behavior of future returns in these markets on the basis of past informations. Similarly, market participants would do well to reassess their investment and risk management framework to mitigate new and somewhat higher levels of risk of their exposures during the turbulent period.Originality/valueTo the authors’ knowledge, this is the first real estate market study employing STL decomposition before applying the MF-DFA in the context of the COVID-19 crisis. Likewise, the study is the first investigation that focuses on these four indexes.

Prediction of air pollutant concentrations based on TCN-BiLSTM-DMAttention with STL decomposition

A model with high accuracy and strong generalization performance is conducive to preventing serious pollution incidents and improving the decision-making ability of urban planning. This paper proposes a new neural network structure based on seasonal–trend decomposition using locally weighted scatterplot smoothing (Loess) (STL) and a dependency matrix attention mechanism (DMAttention) based on cosine similarity to predict the concentration of air pollutants. This method uses STL for series decomposition, temporal convolution, a bidirectional long short-term memory network (TCN-BiLSTM) for feature learning of the decomposed series, and DMAttention for interdependent moment feature emphasizing. In this paper, the long short-term memory network (LSTM) and the gated recurrent unit network (GRU) are set as the baseline models to design experiments. At the same time, to test the generalization performance of the model, short-term forecasts in hours were performed using PM2.5, PM10, SO2, NO2, CO, and O3 data. The experimental results show that the model proposed in this paper is superior to the comparison model in terms of root mean square error (RMSE) and mean absolute percentage error (MAPE). The MAPE values of the 6 kinds of pollutants are 6.800%, 10.492%, 9.900%, 6.299%, 4.178%, and 7.304%, respectively. Compared with the baseline LSTM and GRU models, the average reduction is 49.111% and 43.212%, respectively.

Analyzing the Passenger Traffic Demand Patterns of Greek Ferry Terminals.

Greece is a country with more than 200 inhabited islands, in which almost 17% of population live. Sea transport is the only available connection for the vast majority of these islands. The major ferry network of Greece consists of 155 ports, which are handling on an annual basis more than 35 million passengers. This study uses a panel of secondary data for 155 Greek ports, which were collected for the development of the database of ENIRISST (Intelligent Research Infrastructure for Shipping, Supply Chain, Transport and Logistics) project in order to determine demand patterns. At first, STL decomposition is performed for the throughput timeseries of each port. Afterwards, Gini Index Analysis for Seasonality is performed for all ports. Results are useful for planning of decision-makers and constitute an important addition to currently existing traditional econometric models.