Seasonal Trend Decomposition Using Loess Research Articles

Long-Term Evaluation of Aerosol Optical Properties in the Levantine Region: A Comparative Analysis of AERONET and Aqua/MODIS

The focus on aerosol analysis in the Levantine Region is driven by climate-change impacts, the region’s increasing urban development and industrial activities, and its geographical proximity to major dust-source areas. This study conducts a comparative analysis of aerosol optical depth data from Aqua/MODIS and AERONET during different periods between 2003 and 2023 at four stations: IMS-METU-ERDEMLI (Mersin/Türkiye) (2004–2019), CUT-TEPAK (Limassol/Cyprus) (2010–2023), Cairo_EMA_2 (Cairo/Egypt) (2010–2023), and SEDE_BOKER (Sede Boker/Israel) (2003–2023). The objective is to evaluate the variability and reliability of AOD measurements between satellite and ground-based observations and to determine how well they represent regional climatology. The highest percentage of measurements within the expected error envelope was observed at the IMS-METU-ERDEMLI station, indicating the best agreement between MODIS and AERONET data at this location. The Seasonal-Trend Decomposition using Loess (STL) method revealed consistent spring and summer peaks influenced by dust transport from the Sahara and the Middle East, with lower values in winter. The study also considers the influence of cloud fraction on MODIS measurements and includes aerosol classification. A statistically significant slight positive trend in AOD values was identified at the IMS-METU-ERDEMLI station. Conversely, no significant trends were detected at the other stations. The results of this study agree with those of previous research on the impact of long-range dust transport on regional aerosol loadings, emphasizing the importance of integrating satellite and ground-based observations.

The COVID-19 pandemic in Brazil: space-time approach of cases, deaths, and vaccination coverage (February 2020 – April 2024)

ObjectiveTo assess the evolution of the COVID-19 pandemic in Brazil and its macro-regions, considering disease incidence and mortality rates, as well as identifying territories with still rising disease indices and evaluating vaccine coverage and population adherence to COVID-19 immunization.MethodsAn ecological study conducted in Brazil with COVID-19 cases and deaths reported between February 2020 and April 2024, obtained through the Coronavirus Panel. Historical series were constructed from incidence and mortality rates to assess the pandemic’s evolution, and temporal trends were estimated using the Seasonal Trend Decomposition using Loess (STL) method. The Spatial Variation in Temporal Trends (SVTT) technique was employed to identify clusters with significant variations in temporal trends. Vaccination was analyzed considering the percentage of vaccinated and unvaccinated population in each municipality of the country.ResultsBrazil recorded a total of 38,795,966 cases and 712,038 deaths from COVID-19 during the study period. Incidence and mortality rates showed three waves of the disease, with a fourth wave of smaller amplitude. Four clusters with significant case growth and two with increased deaths were identified. Vaccine coverage varied among municipalities, with some regions showing low vaccination rates and others with high immunization adherence.ConclusionThe study provided a comprehensive overview of coronavirus behavior in Brazil, and its results highlight the ongoing importance of vaccination and the need to direct efforts and resources to areas of higher risk.

The impact of grazing activities and environmental conditions on the stability of alpine grassland ecosystems

Globally, grazing activities have profound impacts on the structure and function of ecosystems. This study, based on a 20-year MODIS time series dataset, employs remote sensing techniques and the Seasonal-Trend decomposition using Loess (STL) algorithm to quantitatively assess the stability of alpine grassland ecosystems from multiple dimensions, and to reveal the characteristics of grazing activities and environmental conditions on ecosystem stability. The results indicate that only 5.77% of the area remains undisturbed, with most areas experiencing varying degrees of disturbance. Further analysis shows that grazing activities in high vegetation coverage areas are the main source of interference. In areas with concentrated interference, elevation and slope have a positive correlation with resistance stability, but a negative correlation with recovery stability. Precipitation and landscape diversity have positive effects on both resistance stability and recovery stability. Vegetation coverage and grazing intensity have a negative correlation with resistance stability, but a positive correlation with recovery stability. This highlights the complex interactions between human activities, environmental factors, and ecosystem stability. The findings emphasize the need for targeted conservation and management strategies to mitigate disturbances to ecosystems affected by human activities and enhance their stability.

Sales forecasting and classification model and pricing research of agricultural perishables based on STL-ARIMA

The prediction of sales volume for agricultural perishable goods is crucial for small-scale merchants to formulate corresponding procurement strategies. Accurate sales volume forecasting helps merchants reduce the risk of excess inventory, establish prudent and appropriate procurement strategies, and provide suggestions for product pricing. To further accurately explore the sales volume patterns of various perishable goods, this study classifies existing data into individual products using the STL (Seasonal-Trend decomposition using Loess) algorithm, revealing the characteristics of each product's sales volume over time. Based on the existing sales volume data, the ARIMA model is used to predict the sales volume of specific categories of goods. A multivariate linear regression model related to pricing, based on existing cost and pricing data, is established to provide merchants with pricing suggestions.

Geographic heterogeneity of activation functions in urban real-time flood forecasting: Based on seasonal trend decomposition using Loess-Temporal Convolutional Network-Gated Recurrent Unit model

Urban real-time flood forecasting is crucial for flood prevention and sustainable development, but it poses challenges due to data inputs and activation functions selection in data-driven models without sufficient focus of geographic heterogeneity. In this study, a novel Seasonal Trend Decomposition using Loess (STL)-Temporal Convolutional Network (TCN)-Gated Recurrent Unit (GRU) model is proposed to improve urban real-time flood forecasting accuracy, twenty-one different activation functions are considered for geographic heterogeneity. Experiments are conducted at six urban drainage system locations in Odense, Denmark. The results show that: (1) STL effectively prepares data for forecasting using TCN and GRU models, leading improved performance compared to single models. STL-TCN-GRU deep learning model demonstrates strong applicability in urban forecasting, achieving an overall accuracy of 0.0079, 0.0140, 0.0482 and 0.9581 in Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Nash-Sutcliffe efficiency coefficient (NSE), respectively. (2) Softsign emerges as the best activation function for forecasting in lower drainage system locations, with average accuracy of 0.0094, 0.0018, 0.0049 and 0.9938 in MAE, RMSE, MAPE and NSE, respectively. Furthermore, Softsign proves to be the best activation function for forecasting in middle drainage system locations, with average accuracy of 0.0047, 0.0081, 0.0309 and 0.9547 in MAE, RMSE, MAPE and NSE, respectively. Swish is the best activation function for forecasting in upper drainage system locations, with average accuracy of 0.0052, 0.0080, 0.0627 and 0.9060 in MAE, RMSE, MAPE and NSE, respectively. This study provides valuable insights for urban real-time flood forecasting modeling with high accuracy and evidence for activation function selection in data-driven models like STL-TCN-GRU for geographic heterogeneity.

Sea Surface Temperature Prediction in China Sea Based on SAM-LSTM Approach

Sea Surface Temperature (SST), a critical environmental element in the ocean, significantly impacts the global atmosphere-ocean energy balance and holds the potential to trigger severe weather like droughts, floods, and El Niño events. Therefore, the prediction of future SST dynamics is crucial to identifying these extreme events and mitigating the damage they caused. In this study, we introduce a time series prediction method based on the Self-Attention Mechanism-Long Short-Term Memory (SAM-LSTM) model. In addition, the historical time-series satellite data of SST anomaly (SSTA) is used instead of SST itself considering that the fluctuations of SST are very small compared to their absolute magnitudes. The Seasonal-Trend decomposition using Loess (STL) method is adopted to decompose the complex non-linear SSTA time series into trend components, seasonal components, and residual components. Then, the deseasonalized time series data at 6 locations in the Bohai Sea are used to train and valid the developed SAM-LSTM model. After that, the validated models are applied to the Yellow Sea, East China Sea, and South China Sea. The experimental results show that the combination of STL time series decomposition and SAM-LSTM can achieve high-precision prediction of daily SSTA than LSTM. This suggests that the methodology used in this paper has a good application for short-term daily SST prediction.

Trend Prediction of Vegetation and Drought by Informer Model Based on STL-EMD Decomposition of Ha Cai Tou Dang Water Source Area in the Maowusu Sandland

To accurately forecast the future development trend of vegetation in dry areas, it is crucial to continuously monitor phenology, vegetation health indices, and vegetation drought indices over an extended period. This is because drought caused by high temperatures significantly affects vegetation. This study thoroughly investigated the spatial and temporal variations in phenological characteristics and vegetation health indices in the abdominal part of Maowusu Sandland in China over the past 20 years. Additionally, it established a linear correlation between vegetation health and temperature indices in the arid zone. To address the issue of predicting long-term trends in vegetation drought changes, we have developed a method that combines the Informer deep learning model with seasonal and Seasonal Trend decomposition using Loess (STL) and empirical mode decomposition (EMD). Additionally, we have utilized the linearly correlated indices of vegetation health and meteorological data spanning 20 years to predict the Normalized Difference Vegetation Index (NDVI) and Temperature Vegetation Dryness Index (TVDI). The study’s findings indicate that over the 20-year observation period, there was an upward trend in NDVI, accompanied by a decrease in both the frequency and severity of droughts. Additionally, the STL-EMD-Informer model successfully predicted the mean absolute percentage error (MAPE = 1.16%) of the future trend in vegetation drought changes for the next decade. This suggests that the overall health of vegetation is expected to continue improving during that time. This work examined the plant growth circumstances in dry locations from several angles and developed a complete analytical method for predicting long-term droughts. The findings provide a strong scientific basis for ecological conservation and vegetation management in arid regions.

A novel hybrid STL-transformer-ARIMA architecture for aviation failure events prediction

Accurate prediction of aviation failure events helps to anticipate future safety situations and protect against further uncontrollable accidents. However, the large sample size, complex temporal characteristics, and significant long-term correlation of aviation failure events increase the operational cost of accurate prediction. To address these challenges, this paper proposes a novel approach involving seasonal-trend decomposition using Loess (STL) and a hybrid prediction model consisting of a transformer and autoregressive integrated moving average (ARIMA). First, STL decomposition is utilized to isolate trend, seasonal, and remainder components, contributing to a comprehensive understanding of the events sample characteristics. The trend component is then trained and predicted using transformer, solving the vanishing gradient problem and improving computational efficiency. ARIMA is employed to train and predict the seasonal and remainder components, maintaining accuracy while reducing complexity. Finally, a comparative evaluation between the proposed and multiple existing approaches is conducted using Aviation Safety Reporting System (ASRS) data. The results demonstrate that the STL-transformer-ARIMA provides more accurate predictions of failure events than single model. It also exhibits significant advantages in robustness and generalization capacity compared to single transformer-based predictors. This revealed that the proposed approach performed better in predicting aviation failure events.

A hybrid deep learning method for the prediction of ship time headway using automatic identification system data

Ship Time Headway (STH) is used in maritime navigation to describe the time interval between the arrivals of two consecutive ships in the same water area. This measurement may offer a straightforward way to gauge the frequency of ship traffic and the likelihood of congestion in a particular area. STH is an important factor in understanding and managing the dynamics of ship movements in busy waterways. This paper introduces a hybrid deep learning method for predicting STH in time domain. The method integrates the Seasonal-Trend Decomposition using Loess (STL), Multi-head Self-Attention (MSA) mechanism into Long Short-Term Memory (LSTM) neural network. The STH dataset was extracted from the Automatic Identification System (AIS) through ship trajectory spatial motion, and the seasonal, trend and residual components of the decomposition were then determined from the STH dataset using the STL algorithms. MSA-LSTM is adopted to comprehensively capture the evolving patterns of STH from the sequence. Comparison studies with existing methods demonstrate the accuracy and robustness of the predictions provided by this method, indicating that the proposed method outperforms other models in terms of prediction performance and learning capabilities. By predicting STH, the method offers potential to assist maritime traffic managers and navigators in assessing ship flow, thereby enabling them to make informed decisions on navigation safety and efficiency.

An intuitive unified hybrid approach for medium to long-term forecasting of different renewable energy sources

Forecasting of stochastic renewable energy resources is quintessential for effective planning, operations and management of the power systems. Existing literature contains ample studies on very short and short-term forecasting of renewables. But it’s still challenging to obtain high accuracy for medium-term and long-term forecasting. Therefore, an intuitive unified hybrid approach is proposed in this paper for medium to long-term forecasting of power generation from different weather-dependent renewables single-handedly by utilising their inherited periodic seasonal patterns iteratively year-on-year basis. Bi-LSTM (Bidirectional Long Short Term Memory) and ARIMA (Auto Regressive Integrated Moving Average) are utilised to construct the proposed approach with the aid of STL (Seasonal-Trend decomposition using Loess) decomposition and data pre-processing. The performance of proposed approach (STL-ARIMA-BiLSTM) is validated using seven recent datasets of wind, solar and hydro power. It yields accurate forecasts for a week-ahead to a year-ahead forecasting horizons. MAE (Mean Absolute Error) lying in range from 6.3% to 6.6%, 5.6% to 6.7% and 4.72% for a year-ahead forecast of wind, hydro and solar power, respectively, is obtained. It is established that these long-term forecast errors are even less than the short-term forecast errors of some of the existing studies demonstrating novelty and practicality of the proposed approach.

Prediction of soil moisture using BiGRU-LSTM model with STL decomposition in Qinghai-Tibet Plateau.

Ali Network data based on the Qinghai-Tibetan Plateau (QTP) can provide representative coverage of the climate and surface hydrometeorological conditions in the cold and arid region of the QTP. Among them, the plateau soil moisture can effectively quantify the uncertainty of coarse resolution satellite and soil moisture models. With the objective of constructing an "end-to-end" soil moisture prediction model for the Tibetan Plateau, a combined prediction model based on time series decomposition and a deep neural network is proposed in this article. The model first performs data preprocessing and seasonal-trend decomposition using loess (STL) to obtain the trend component, seasonal component and random residual component of the original time series in an additive way. Subsequently, the bidirectional gated recurrent unit (BiGRU) is used for the trend component, and the long short-term memory (LSTM) is used for the seasonal and residual components to extract the time series information. The experiments based on the measured data demonstrate that the use of STL decomposition and the combination model can effectively extract the information in soil moisture series using its concise and clear structure. The proposed model in this article has a stable performance improvement of 5-30% over a single model and existing prediction models in different prediction time domains. In long-range prediction, the proposed model also achieves the best accuracy in the shape and temporal domains described by using dynamic time warping (DTW) index and temporal distortion index (TDI). In addition, the generalization performance experiments show that the combined method proposed in this article has strong reference value for time series prediction of natural complex systems.

STL-decomposition ensemble deep learning models for daily reservoir inflow forecast for hydroelectricity production

Accurate reservoir inflow forecasting is crucial for efficient water management. In this study, different deep learning models, including Dense, Long short-term memory (LSTM), and one-dimensional convolutional neural networks (Conv1D), were used to build ensembles. Seasonal-trend decomposition using loess (STL) was applied to decompose reservoir inflows and precipitations into random, seasonal, and trend components. Seven ensemble models, namely STL-Dense, STL-Conv1D, STL-LSTM, STL-Dense-LSTM-Conv1D, STL-Dense multivariate, STL-LSTM multivariate, and STL-Conv1D multivariate, were proposed and evaluated using daily inflows and precipitation decomposed data from the Lom Pangar reservoir from 2015 to 2020. Evaluation metrics, such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Nash Sutcliff Efficiency (NSE), were applied to assess model performance. Results showed that the STL-Dense multivariate model was the best ensemble among the thirteen models with MAE of 14.636 m3/s, RMSE of 20.841 m3/s, MAPE of 6.622%, and NSE of 0.988. These findings stress the importance of considering multiple inputs and models for accurate reservoir inflow forecasting and optimal water management. Not all ensemble models were good for Lom pangar inflow forecast as the Dense, Conv1D, and LSTM models performed better than their proposed STL monovariate ensemble models.

Study on the prediction effect of a combined model of SARIMA and LSTM based on SSA for influenza in Shanxi Province, China

BackgroundInfluenza is an acute respiratory infectious disease that is highly infectious and seriously damages human health. Reasonable prediction is of great significance to control the epidemic of influenza.MethodsOur Influenza data were extracted from Shanxi Provincial Center for Disease Control and Prevention. Seasonal-trend decomposition using Loess (STL) was adopted to analyze the season characteristics of the influenza in Shanxi Province, China, from the 1st week in 2010 to the 52nd week in 2019. To handle the insufficient prediction performance of the seasonal autoregressive integrated moving average (SARIMA) model in predicting the nonlinear parts and the poor accuracy of directly predicting the original sequence, this study established the SARIMA model, the combination model of SARIMA and Long-Short Term Memory neural network (SARIMA-LSTM) and the combination model of SARIMA-LSTM based on Singular spectrum analysis (SSA-SARIMA-LSTM) to make predictions and identify the best model. Additionally, the Mean Squared Error (MSE), Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) were used to evaluate the performance of the models.ResultsThe influenza time series in Shanxi Province from the 1st week in 2010 to the 52nd week in 2019 showed a year-by-year decrease with obvious seasonal characteristics. The peak period of the disease mainly concentrated from the end of the year to the beginning of the next year. The best fitting and prediction performance was the SSA-SARIMA-LSTM model. Compared with the SARIMA model, the MSE, MAE and RMSE of the SSA-SARIMA-LSTM model decreased by 38.12, 17.39 and 21.34%, respectively, in fitting performance; the MSE, MAE and RMSE decreased by 42.41, 18.69 and 24.11%, respectively, in prediction performances. Furthermore, compared with the SARIMA-LSTM model, the MSE, MAE and RMSE of the SSA-SARIMA-LSTM model decreased by 28.26, 14.61 and 15.30%, respectively, in fitting performance; the MSE, MAE and RMSE decreased by 36.99, 7.22 and 20.62%, respectively, in prediction performances.ConclusionsThe fitting and prediction performances of the SSA-SARIMA-LSTM model were better than those of the SARIMA and the SARIMA-LSTM models. Generally speaking, we can apply the SSA-SARIMA-LSTM model to the prediction of influenza, and offer a leg-up for public policy.

THE NEXUS BETWEEN TWITTER-BASED UNCERTAINTY AND CRYPTOCURRENCIES: A MULTIFRACTAL ANALYSIS

We take the novel Twitter-based economic uncertainty (TEU) to examine if it has cross-correlation characteristics with four major cryptocurrencies i.e. Bitcoin, Ethereum, Litecoin, and Ripple. To conduct a more thorough analysis, we apply multifractal detrended cross-correlation analysis (MFDCCA) on seasonal-trend decomposition using Loess (STL) decomposed series as well as without decomposed series on the daily data, ranging from 1 June 2011 to 30 June 2021. The findings of this study indicate that: (i) all pairs of TEU with cryptocurrencies are multifractal and have power-law behavior; (ii) the pairs of Ethereum and Bitcoin with TEU are found to be the most multifractal while Litecoin with TEU has the lowest multifractal characteristics; (iii) all STL decomposed series of cryptocurrency have persistent cross-correlation with TEU with the exception of Ethereum which has anti-persistent cross-correlation with TEU; (iv) all without decomposed series of cryptocurrencies show significant persistent cross-correlation characteristics with TEU; (v) the highest linkage is found for the pair of Bitcoin with TEU. Moreover, to reveal the dynamic characteristics in the cross-correlation of TEU with cryptocurrencies, the rolling window is employed for MFDCCA. These findings have important managerial and academic implications for policymakers, investors, and market participants.

Impact of COVID-19 on Tuberculosis Indicators in Brazil: A Time Series and Spatial Analysis Study.

Background: We aimed to visualize and classify the time series of COVID-19, tuberculosis (TB) notification, and TB outcomes (cure, treatment abandonment, and death), verify the impact of the new coronavirus pandemic on these indices in Brazil, and verify the presence of spatial autocorrelation between COVID-19 and TB. Methods: This was an ecological time series study that considered TB and COVID-19 cases. Seasonal Trend Decomposition using Loess (STL) was used to trace the temporal trend, Prais–Winsten was used to classify the temporal trend, Interrupted Time Series (ITS) was used to verify the impact of COVID-19 on TB rates, and the Bivariate Moran Index (Global and Local) was used to verify the spatial autocorrelation of events. Results: Brazil and its macro-regions showed an increasing temporal trend for the notification of TB in the pre-pandemic period. Only the Northeast Region showed a decreasing temporal trend for cured cases. For treatment abandonment, all regions except for the Northeast showed an increasing temporal trend, and regarding death, Brazil and the Northeast Region showed an increasing temporal trend. With the ITS, COVID-19 caused a decline in TB notification rates and TB outcome rates. With the global spatial analysis, it was possible to identify the existence of spatial autocorrelation between the notification rate of COVID-19 and the TB notification rate and deaths. With the local analysis, it was possible to map the Brazilian municipalities and classify them according to the relationship between the rates of both diseases and space. Conclusions: COVID-19 influenced the follow-up of and adherence to TB treatment and intensified social vulnerability and, consequently, affected the notification of TB since the relationship between the disease and social determinants of health is already known. The restoration and strengthening of essential services for the prevention and detection of cases and treatment of TB in endemic environments such as Brazil have been oriented as a priority in the global health agenda.

User-Aware and Flexible Proactive Caching Using LSTM and Ensemble Learning in IoT-MEC Networks

To meet the stringent demands of emerging Internet-of-Things (IoT) applications, such as smart home, smart city, and virtual reality in 5G/6G IoT networks, edge content caching for mobile/multiaccess edge computing (MEC) has been identified as a promising approach to improve the quality of services in terms of latency and energy consumption. However, the limitations of cache capacity make it difficult to develop an effective common caching framework that satisfies diverse user preferences. In this article, we propose a new content caching strategy that maximizes the cache hit ratio through flexible prediction in dynamically changing network and user environments. It is based on a hierarchical deep learning architecture: long short-term memory (LSTM)-based local learning and ensemble-based meta-learning. First, as a local learning model, we employ an LSTM method with seasonal-trend decomposition using loess (STL)-based preprocessing. It identifies the attributes for demand prediction on the contents in various demographic user groups. Second, as a metalearning model, we employ a regression-based ensemble learning method, which uses an online convex optimization framework and exhibits sublinear “regret” performance. It orchestrates the obtained multiple demographic user preferences into a unified caching strategy in real time. Extensive experiments were conducted on the popular MovieLens data sets. It was shown that the proposed control provides up to a 30% higher cache hit ratio than conventional representative algorithms and a near-optimal cache hit ratio within approximately 9% of the optimal caching scheme with perfect prior knowledge of content popularity. The proposed learning and caching control can be implemented as a core function of the 5G/6G standard’s network data analytic function (NWDAF) module.

MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns

The decomposition of time series into components is an important task that helps to understand time series and can enable better forecasting. Nowadays, with high sampling rates leading to high-frequency data (such as daily, hourly, or minutely data), many real-world datasets contain time series data that can exhibit multiple seasonal patterns. Although several methods have been proposed to decompose time series better under these circumstances, they are often computationally inefficient or inaccurate. In this study, we propose Multiple Seasonal-Trend decomposition using Loess (MSTL), an extension to the traditional Seasonal-Trend decomposition using Loess (STL) procedure, allowing the decomposition of time series with multiple seasonal patterns. In our evaluation on synthetic and a perturbed real-world time series dataset, compared to other decomposition benchmarks, MSTL demonstrates competitive results with lower computational cost. The implementation of MSTL is available in the R package forecast.

Cross-correlations between economic policy uncertainty and precious and industrial metals: A multifractal cross-correlation analysis

This study combines Seasonal-Trend decomposition using LOESS (STL) and multifractal cross-correlation analysis (MFCCA) to estimate the cross-correlations between the evolution of the economic policy uncertainty (EPU) of the USA and return of precious and industrial metals. Based on daily closing values of EPU and eight metals ranging from 01-Jan-2010 to 02-May-2021, the empirical findings confirm the presence of nonlinear dependencies, based on all EPU-Metal relationships, suggesting that EPU and metal markets are interlinked. Furthermore, there is evidence of multifractality, although with a varying degree, between EPU and metal markets. The strongest multifractality is found in EPU-Tin and EPU-Silver, while EPU-Platinum and EPU-Gold exhibit the weakest multifractality. Precious metals show persistent cross-correlations while industrial metals have anti-persistent cross-correlations with EPU, with that cross-correlation behavior being more persistent in the case of small fluctuations, which have different implications for the different market agents.

MuSDRI: Multi-Seasonal Decomposition Based Recurrent Imputation for Time Series

Missing values are a common problem of time series such as sensor-generated data due to issues of data collection, transmission, and storage. To deal with this problem, various data imputation methods have been proposed. Among these methods, variants of recurrent neural networks (RNNs) have attracted a lot of attention as they provide a natural representation of temporal dynamics. Though such methods have been shown to achieve higher imputation accuracy, they mostly focus on the modeling of temporal dynamics from a short-term perspective while ignoring the long-term features such as trend and seasonal information embedded in time series data. In this paper, we investigate different paradigms of time series imputation methods to capture temporal dynamics from both long-term and short-term perspectives. In particular, we propose a new learning paradigm called MuSDRI which combines the time series decomposition method Seasonal Trend decomposition using Loess (STL) with RNNs. Specifically, STL is used to decompose long sequences of time series into trend, seasonal, and remainder components such that long-term dynamics can be revealed; RNNs are used to capture local patterns from the remainder component extracted by STL such that short-term dynamics can be refined. Moreover, MuSDRI is able to handle time series with multiple seasonal patterns by learning their contributions with respect to the imputation task. We evaluate the proposed imputation methods on three real-world datasets. Experimental results show that the imputation methods considering both the long-term and short-term dynamics achieve higher imputation accuracy, and among them MuSDRI in general achieves the best performance.

The Impact of Seasonality and Response Period on Qualifying the Relationship between Ecosystem Productivity and Climatic Factors over the Eurasian Steppe

As climate change intensifies, surface vegetation productivity and carbon exchange between terrestrial ecosystems and the atmosphere are significantly affected by the variation of climatic factors. Due to the sensitivity of grasslands to these climatic factors, it is crucial to understand the response of vegetation greenness, or carbon exchange within grasslands, to environment factor dynamics. In this study, we used solar-induced chlorophyll fluorescence (SIF), precipitation (P), vapor pressure deficit (VPD), evaporative stress (ES), and root zone soil moisture (RSM) derived from remote sensing, reanalysis, and assimilation datasets to explore the response of vegetation greenness within Eurasian Steppe to climatic factors. Our results indicated deseasonlization based on the Seasonal-Trend decomposition using Loess (STL) method, which was an effective means to remove the seasonality disturbances that affect the qualification of the relationship between SIF and the four climatic factors. The response of SIF had a time lag effect on these climatic factors, and the longer the response period, the greater the impact on the correlation of SIF with P, VPD, ES, and RSM. We also found, among the four factors, that the response of SIF to ES was the timeliest. The findings of this study emphasized the impact of the seasonality and time lag effect on the dynamic response between variables, and provided references to the attribution and monitoring of vegetation greenness and ecosystem productivity.