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Keywords = seasonal and trend decomposition

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33 pages, 3187 KiB  
Article
Predicting Firm’s Performance Based on Panel Data: Using Hybrid Methods to Improve Forecast Accuracy
by Nikita V. Martyushev, Vladislav Spitsin, Roman V. Klyuev, Lubov Spitsina, Vladimir Yu. Konyukhov, Tatiana A. Oparina and Aleksandr E. Boltrushevich
Mathematics 2025, 13(8), 1247; https://doi.org/10.3390/math13081247 - 10 Apr 2025
Viewed by 97
Abstract
The problem of predicting profitability is exceptionally relevant for investors and company owners making decisions about investment and business development. The global literature contains a number of studies where researchers predict the profitability of firms using various methods, including modern machine learning. However, [...] Read more.
The problem of predicting profitability is exceptionally relevant for investors and company owners making decisions about investment and business development. The global literature contains a number of studies where researchers predict the profitability of firms using various methods, including modern machine learning. However, these works hardly take advantage of panel data. This paper takes advantage of additional capabilities offered by panel data and proposes hybrid forecasting methods based on panel data, which allow significantly improving the accuracy of predicting the profitability. Our calculations show that when predicting the profitability, investors and company owners should take into account the profitability of the previous years and the trend in its change. The work shows that this approach can be successfully applied to high-tech companies whose profitability is characterised by increased volatility. Prediction forecasting includes STL-decomposition of time series, regression with random effects and machine learning (LSTM and CatBoost), and clustering. The training sample includes 1811 companies and data for 2013–2018 (panel data, 10,866 observations). The test sample contains data for these companies for 2019. As a result, the authors propose an approach significantly improving the accuracy of predicting ROA and ROE based on the panel nature of the data. The panel data allowed using the profitability of the previous years in forecast models and applying the STL-decomposition of the profitability of the previous years into three variables (Trend, Seasonal, and Residual), considerably improving the quality of the constructed forecast models (STL-CatBoost, STL-LSTM, and STL-RE hybrid models). Full article
(This article belongs to the Special Issue Advances in Theoretical and Empirical Economic Modeling)
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16 pages, 4555 KiB  
Article
Statistical Approach for the Imputation of Long-Term Seawater Data Around the Korean Peninsula from 1966 to 2021
by Myeong-Taek Kwak, Kyunghwan Lee, Hyi-Thaek Ceong and Seungwon Oh
Water 2025, 17(7), 1066; https://doi.org/10.3390/w17071066 - 3 Apr 2025
Viewed by 69
Abstract
Climate change is a global phenomenon that significantly impacts the ocean environment around the Korean Peninsula. These changes in climate can lead to rising sea temperatures, thereby significantly affecting marine life and ecosystems in the region. In this study, four statistical approaches were [...] Read more.
Climate change is a global phenomenon that significantly impacts the ocean environment around the Korean Peninsula. These changes in climate can lead to rising sea temperatures, thereby significantly affecting marine life and ecosystems in the region. In this study, four statistical approaches were employed to analyze ocean characteristics around the Korean Peninsula: layer classification, imputation for replacing missing values, evaluation using statistical tests, and trend analysis. The trend model we used was a deep learning-based seasonal-trend decomposition using Loess, a piecewise regression module with change points in 2000 and 2009, and Fourier transform to calculate the seasonality of one year. In addition, the water temperature was considered to have a Gaussian distribution so that anomalous water temperatures could be detected through confidence intervals. The ocean was first classified into three layers (surface layer, middle layer, and bottom layer) to characterize the sea area around Korea, after which multiple imputation methods were employed to replace missing values for each layer. The imputation method exhibiting the best performance was then selected by comparing the replaced missing values with high-quality data. Additionally, we compared the slope of the water temperature change around the Korean Peninsula based on two temporal inflection points (2000 and 2009). Our findings demonstrated that the long-term change in water temperature aligns with previous studies. However, the slope of the water temperature change has tended to accelerate since 2009. Full article
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19 pages, 3796 KiB  
Article
Modeling and Forecasting Time-Series Data with Multiple Seasonal Periods Using Periodograms
by Solomon Buke Chudo and Gyorgy Terdik
Econometrics 2025, 13(2), 14; https://doi.org/10.3390/econometrics13020014 - 28 Mar 2025
Viewed by 196
Abstract
Applications of high-frequency data, including energy management, economics, and finance, frequently require time-series forecasting characterized by complex seasonality. Recognizing prevailing seasonal trends continues to be difficult, given that the majority of solutions depend on basic decomposition techniques. This study introduces a new approach [...] Read more.
Applications of high-frequency data, including energy management, economics, and finance, frequently require time-series forecasting characterized by complex seasonality. Recognizing prevailing seasonal trends continues to be difficult, given that the majority of solutions depend on basic decomposition techniques. This study introduces a new approach employing periodograms from spectral density analysis to identify predominant seasonal periods. When analyzing hourly electricity consumption data from Brazil, we identified three significant seasonal patterns: sub-daily (6 h), half-daily (12 h), and daily (24 h). We assessed the predictive efficacy of the BATS, TBATS, and STL + ETS models using these seasonal periods. We performed data analysis and model fitting in R 4.4.1 and used accuracy metrics like MAE, MAPE, and others to compare the models. The STL + ETS model exhibited an enhanced performance, surpassing both BATS and TBATS in energy forecasting. These findings improve our understanding of multiple seasonal patterns, assist us in selecting dominating periods, provide new practical forecasting approaches for time-series analysis, and inform professionals seeking superior forecasting solutions in various fields. Full article
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29 pages, 3575 KiB  
Article
Linear Model and Gradient Feature Elimination Algorithm Based on Seasonal Decomposition for Time Series Forecasting
by Sheng-Tzong Cheng, Ya-Jin Lyu and Yi-Hong Lin
Mathematics 2025, 13(5), 883; https://doi.org/10.3390/math13050883 - 6 Mar 2025
Viewed by 362
Abstract
In the wave of digital transformation and Industry 4.0, accurate time series forecasting has become critical across industries such as manufacturing, energy, and finance. However, while deep learning models offer high predictive accuracy, their lack of interpretability often undermines decision-makers’ trust. This study [...] Read more.
In the wave of digital transformation and Industry 4.0, accurate time series forecasting has become critical across industries such as manufacturing, energy, and finance. However, while deep learning models offer high predictive accuracy, their lack of interpretability often undermines decision-makers’ trust. This study proposes a linear time series model architecture based on seasonal decomposition. The model effectively captures trends and seasonality using an additive decomposition, chosen based on initial data visualization, indicating stable seasonal variations. An augmented feature generator is introduced to enhance predictive performance by generating features such as differences, rolling statistics, and moving averages. Furthermore, we propose a gradient-based feature importance method to improve interpretability and implement a gradient feature elimination algorithm to reduce noise and enhance model accuracy. The approach is validated on multiple datasets, including order demand, energy load, and solar radiation, demonstrating its applicability to diverse time series forecasting tasks. Full article
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23 pages, 13510 KiB  
Article
Assessing the Role of Energy Mix in Long-Term Air Pollution Trends: Initial Evidence from Poland
by Mateusz Zareba
Energies 2025, 18(5), 1211; https://doi.org/10.3390/en18051211 - 1 Mar 2025
Viewed by 432
Abstract
Air pollution remains a critical environmental and public health issue, requiring diverse research perspectives, including those related to energy production and consumption. This study examines the relationship between Poland’s energy mix and air pollution trends by integrating national statistical data on primary energy [...] Read more.
Air pollution remains a critical environmental and public health issue, requiring diverse research perspectives, including those related to energy production and consumption. This study examines the relationship between Poland’s energy mix and air pollution trends by integrating national statistical data on primary energy consumption and renewable energy sources over the past 15 years with air pollution measurements from the last eight years. The air pollution data, obtained from reference-grade monitoring stations, focus on particulate matter (PM). To address discrepancies in temporal resolution between daily PM measurements and annual energy sector reports, a bootstrapping method was applied within a regression framework to assess the overall impact of individual energy components on national air pollution levels. Seasonal decomposition techniques were employed to analyze the temporal dynamics of specific energy sources and their contributions to pollution variability. A key aspect of this research is the role of renewable energy sources in air quality trends. This study also investigates regional variations in pollution levels by analyzing correlations between geographic location, industrialization intensity, and the proportion of green areas across Poland’s administrative regions (Voivodeships). This spatially explicit approach provides deeper insights into the linkages between energy production and pollution distribution at a national scale. Poland presents a unique case due to its distinct energy mix, which differs significantly from the EU average, its persistently high air pollution levels, and recent regulatory changes. These factors create an ideal setting to assess the impact of energy sector transitions on environmental quality. By employing high-resolution spatiotemporal big data analysis, this study leverages measurements from over 100 monitoring stations and applies advanced statistical methodologies to integrate multi-scale energy and pollution datasets. From a PM perspective, the regression analysis showed that High-Methane Gas had a neutral impact on PM concentrations, making it a suitable transition energy source, while renewables exhibited negative regression coefficients and coal-based sources showed positive coefficients. The findings offer new perspectives on the long-term environmental effects of shifts in national energy policies. Full article
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13 pages, 2924 KiB  
Article
Temporal Variations in Rice Water Requirements and the Impact of Effective Rainfall on Irrigation Demand: Strategies for Sustainable Rice Cultivation
by Shijiang Zhu, Wenjie Tong, Hu Li, Kaikai Li, Wen Xu and Baocui Liang
Water 2025, 17(5), 656; https://doi.org/10.3390/w17050656 - 24 Feb 2025
Viewed by 481
Abstract
In response to increasing global food demand and the significant water requirements of rice cultivation, this study aims to enhance water use efficiency in rice farming. Focusing on Jiayu County, a subtropical humid region in China, where rice is grown as a single [...] Read more.
In response to increasing global food demand and the significant water requirements of rice cultivation, this study aims to enhance water use efficiency in rice farming. Focusing on Jiayu County, a subtropical humid region in China, where rice is grown as a single crop every year, we investigated temporal variations in rice water requirements and the influence of effective rainfall on irrigation strategies. Data were collected from an experimental station within the Sanhulianjiang Reservoir in Jiayu County. Utilizing the Mann–Kendall trend test and the Seasonal–Trend Decomposition using the LOESS (STL) method, we analyzed historical data on rice water requirement (ETc) and effective rainfall (Re ). Our findings reveal that annual water requirements for rice range between 432 mm and 746 mm, with peaks corresponding to critical growth stages such as tillering and jointing–booting. Effective rainfall contributes significantly to meeting these needs, providing 27–35% of the total water requirement during specific periods. Developed water-saving irrigation strategies, including optimized irrigation scheduling and the introduction of drought-resistant rice varieties, demonstrate a potential reduction in irrigation demands by approximately 33.84%. This study underscores the importance of integrating effective rainfall data into irrigation practices to enhance water use efficiency and promote sustainable rice production amidst climate variability challenges. Full article
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25 pages, 18040 KiB  
Article
A Novel BiGRU-Attention Model for Predicting Corn Market Prices Based on Multi-Feature Fusion and Grey Wolf Optimization
by Yang Feng, Xiaonan Hu, Songsong Hou and Yan Guo
Agriculture 2025, 15(5), 469; https://doi.org/10.3390/agriculture15050469 - 21 Feb 2025
Viewed by 446
Abstract
Accurately predicting corn market prices is crucial for ensuring corn production, enhancing farmers’ income, and maintaining the stability of the grain market. However, corn price fluctuations are influenced by various factors, exhibiting non-stationarity, nonlinearity, and high volatility, making prediction challenging. Therefore, this paper [...] Read more.
Accurately predicting corn market prices is crucial for ensuring corn production, enhancing farmers’ income, and maintaining the stability of the grain market. However, corn price fluctuations are influenced by various factors, exhibiting non-stationarity, nonlinearity, and high volatility, making prediction challenging. Therefore, this paper proposes a comprehensive, efficient, and accurate method for predicting corn prices. First, in the data processing phase, the seasonal and trend decomposition using LOESS (STL) algorithm was used to extract the trend, seasonality, and residual components of corn prices, combined with the GARCH-in-mean (GARCH-M) model to delve into the volatility clustering characteristics. Next, the kernel principal component analysis (KPCA) was employed for nonlinear dimensionality reduction to extract key information and accelerate model convergence. Finally, a BiGRU-Attention model, optimized by the grey wolf optimizer (GWO), was constructed to predict corn market prices accurately. The effectiveness of the proposed model was assessed through cross-sectional and longitudinal validation experiments. The empirical results indicated that the proposed STLG-KPCA-GWO-BiGRU-Attention (SGKGBA) model exhibited significant advantages in terms of MAE (0.0159), RMSE (0.0215), MAPE (0.5544%), and R2 (0.9815). This model effectively captures price fluctuation features, significantly enhances prediction accuracy, and offers reliable trend forecasts for decision makers regarding corn market prices. Full article
(This article belongs to the Section Agricultural Economics, Policies and Rural Management)
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21 pages, 3134 KiB  
Article
Deep Learning for Demand Forecasting: A Framework Incorporating Variational Mode Decomposition and Attention Mechanism
by Chunrui Lei, Heng Zhang, Zhigang Wang and Qiang Miao
Processes 2025, 13(2), 594; https://doi.org/10.3390/pr13020594 - 19 Feb 2025
Viewed by 535
Abstract
Accurate demand forecasting is crucial for modern supply chain management, forming the foundation for inventory optimization, cost control, and service level improvement. However, demand time series data often exhibit high volatility and diverse patterns, further complicated by the rapid expansion and heterogeneity of [...] Read more.
Accurate demand forecasting is crucial for modern supply chain management, forming the foundation for inventory optimization, cost control, and service level improvement. However, demand time series data often exhibit high volatility and diverse patterns, further complicated by the rapid expansion and heterogeneity of data sources. These challenges can result in significant degradation in predictive accuracy when traditional models are applied to complex demand datasets. To address these challenges, this study proposes an end-to-end demand forecasting framework leveraging Variational Mode Decomposition (VMD) and attention mechanisms. The framework first employs VMD to decompose raw demand time series into multiple modes to extract hierarchical features, including trends, seasonal patterns, and short-term variations. Subsequently, an attention mechanism is introduced to dynamically capture and integrate demand sequences alongside contextual information, enhancing the focus on critical features and improving predictive performance. Experimental results demonstrate that the proposed method achieves superior predictive accuracy compared to conventional approaches, with a 37% reduction in Mean Absolute Error (MAE) relative to baseline models. This substantial improvement in demand forecasting accuracy provides actionable insights for decision-makers, enabling more efficient inventory control, production planning, and overall supply chain optimization. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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16 pages, 6008 KiB  
Article
Spatial and Temporal Variations of Vegetation Water Content Using VOD and VPD in China During 2000–2016
by Yibing Sun, Zhaodan Cao, Chengqiu Wu and Xiaoer Zhao
Water 2025, 17(4), 568; https://doi.org/10.3390/w17040568 - 15 Feb 2025
Viewed by 648
Abstract
Vegetation water content, characterized by vapor pressure deficit (VPD) and vegetation optical depth (VOD), can represent vegetation health in terrestrial ecosystems. In this study, using remote sensing Ku-band VOD and VPD, the spatiotemporal distribution assessment, Mann-Kendall trend analysis, seasonal trend decomposition, and correlation [...] Read more.
Vegetation water content, characterized by vapor pressure deficit (VPD) and vegetation optical depth (VOD), can represent vegetation health in terrestrial ecosystems. In this study, using remote sensing Ku-band VOD and VPD, the spatiotemporal distribution assessment, Mann-Kendall trend analysis, seasonal trend decomposition, and correlation analysis and significance testing were conducted to investigate the spatiotemporal distribution patterns, seasonal variations and correlations of VPD and VOD across China from 2000 to 2016. And the correlation between climate factors (temperature and precipitation) with VOD and VPD was discussed. The results show the following: (1) The annual mean VPD in China predominantly ranged from 0 to 4 KPa, while the annual mean VOD were centered around 0 to 2 during 2000–2016. Spatially, the VOD peaked at 1–2 in southwest China. VPD have significant seasonal variations across China, with high VPD in the summer. (2) The VPD and VOD in most regions of China fluctuated and showed an upward trend from 2000 to 2016, with significantly increased VPD in northwest and southwest China. (3) On a monthly scale, regions where VOD positively correlated with VPD accounted for 89.69% of the total area of China. The proportion of areas with a significant positive correlation was 82.96%. The proportion of areas with a negative correlation was 10.31%, and the proportion of areas with a significant negative correlation was 5.41%. Annual VOD and VPD exhibited a positive correlation of 61.28% of China’s total territory. Among these, the area exhibiting a significant positive correlation made up 6.15%. The area demonstrating a negative correlation amounted to 38.72%, and the area with a significant negative correlation constituted 2.22%. This study can contribute to understanding vegetation water content dynamics across China, which is crucial for ecosystem sustainability in China. Full article
(This article belongs to the Section Ecohydrology)
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9 pages, 3322 KiB  
Proceeding Paper
Integrating Time Series Decomposition and Deep Learning: An STL-TCN-Transformer Framework for Landslide Displacement Prediction
by Shuai Ren and Kamarul Hawari Ghazali
Eng. Proc. 2025, 84(1), 60; https://doi.org/10.3390/engproc2025084060 - 13 Feb 2025
Cited by 2 | Viewed by 262
Abstract
Accurate prediction of landslide displacement is crucial for disaster prevention and mitigation. This study proposes an STL-TCN-Transformer model that combines time series decomposition with deep learning to predict cumulative displacement. Using monitoring data from the Baishuihe landslide, the displacement sequence was decomposed into [...] Read more.
Accurate prediction of landslide displacement is crucial for disaster prevention and mitigation. This study proposes an STL-TCN-Transformer model that combines time series decomposition with deep learning to predict cumulative displacement. Using monitoring data from the Baishuihe landslide, the displacement sequence was decomposed into trend, periodic, and residual components using the STL method. The trend component, determined by geotechnical properties, was predicted using a univariate TCN-Transformer, while the periodic and residual components, influenced by rainfall and reservoir water levels, were analyzed for nonlinear correlations using the Spearman method and predicted with a multivariate TCN-Transformer. The proposed model achieved superior performance, with R2 of 0.993, RMSE of 7.82 mm, and MAE of 5.82 mm, significantly outperforming EMD-LSTM, EEMD-RNN, and VMD-BiLSTM models in all metrics. These findings demonstrate the ability of the STL-TCN-Transformer to effectively capture the dynamics of landslide displacement, offering a reliable approach for landslide monitoring and early warning systems. Full article
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23 pages, 1112 KiB  
Article
STL-DCSInformer-ETS: A Hybrid Model for Medium- and Long-Term Sales Forecasting of Fast-Moving Consumer Goods
by Yecheng Ma, Lili He and Junhong Zheng
Appl. Sci. 2025, 15(3), 1516; https://doi.org/10.3390/app15031516 - 2 Feb 2025
Cited by 1 | Viewed by 625
Abstract
Accurately forecasting sales for fast-moving consumer goods (FMCG) remains a significant challenge due to the volatile and multi-faceted nature of sales data. Existing methods often struggle to capture intricate patterns driven by seasonal trends, external factors, and consumer behavior, hindering effective inventory management [...] Read more.
Accurately forecasting sales for fast-moving consumer goods (FMCG) remains a significant challenge due to the volatile and multi-faceted nature of sales data. Existing methods often struggle to capture intricate patterns driven by seasonal trends, external factors, and consumer behavior, hindering effective inventory management and strategic decision-making. To overcome these challenges, we propose STL-DCSInformer-ETS, a hybrid model that integrates three complementary components: STL decomposition, an enhanced DCSInformer model, and the ETS model. The model uses monthly sales data from a FMCG company, with key features including sales volume, product prices, promotional activities, and regulatory factors such as holidays, geographical information, consumer behavior, product factors, etc. STL decomposition partitions time-series data into trend, seasonal, and residual components, reducing data complexity and enabling more targeted forecasting. The enhanced DCSInformer employs dilated causal convolution and a multi-scale feature extraction mechanism to capture long-term dependencies and short-term variations effectively. Meanwhile, the ETS model specializes in modeling seasonal patterns, further refining forecasting precision. To further improve predictive performance, the Random Forest-based Recursive Feature Elimination (RF-RFE) method is applied to optimize feature selection. RF-RFE identifies key predictive factors from multiple dimensions, such as time, geography, and economy, which significantly influence forecasting accuracy. Through numerical experiments, the method demonstrates excellent performance by achieving a 35.9% reduction in Mean Squared Error and a 21.4% decrease in Mean Absolute Percentage Error, significantly outperforming traditional methods. Furthermore, the model effectively captures both medium- and long-term sales trends while addressing short-term fluctuations, leading to more accurate forecasting and improved decision-making for fast-moving consumer goods. This research provides new theoretical insights into hybrid forecasting models and practical solutions for optimizing inventory management and strategic planning in the FMCG industry. Full article
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19 pages, 15109 KiB  
Article
A Time Series Decomposition-Based Interpretable Electricity Price Forecasting Method
by Yuanke Cu, Kaishu Wang, Lechen Zhang, Zixuan Liu, Yixuan Liu and Li Mo
Energies 2025, 18(3), 664; https://doi.org/10.3390/en18030664 - 31 Jan 2025
Viewed by 592
Abstract
Electricity price forecasting is of significant practical importance, and improving prediction accuracy has become a key area of focus. Although substantial progress has been made in electricity price forecasting research, the unique characteristics of the electricity market make prices highly sensitive to even [...] Read more.
Electricity price forecasting is of significant practical importance, and improving prediction accuracy has become a key area of focus. Although substantial progress has been made in electricity price forecasting research, the unique characteristics of the electricity market make prices highly sensitive to even minor market changes. This results in prices exhibiting long-term trends while also experiencing sharp fluctuations due to sudden events, often leading to extreme values. Furthermore, most current models are “black-box” models, lacking transparency and interpretability. These unique features make electricity price forecasting particularly complex and challenging. This paper introduces a forecasting framework that incorporates the Seasonal Trend decomposition using Loess (STL), Gated Recurrent Unit (GRU), Light Gradient Boosting Machine (LightGBM), and Shapley Additive Explanations (SHAPs) and applies it to forecasting in the electricity markets of the United States and Australia. The proposed forecasting framework significantly improves prediction accuracy compared to nine other baseline models, especially in terms of RMSE and R2 metrics, while also providing clear insights into the factors influencing the forecasts. On the U.S. dataset, the RMSE of this framework is 12.7% lower than that of the second-best model, while, on the Australian dataset, the RMSE of the SLGSEF is 2.58% lower than that of the second-best model. Full article
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21 pages, 14702 KiB  
Article
Detecting the Phenological Threshold to Assess the Grassland Restoration in the Nanling Mountain Area of China
by Zhenhuan Liu, Sujuan Li and Yueteng Chi
Remote Sens. 2025, 17(3), 451; https://doi.org/10.3390/rs17030451 - 28 Jan 2025
Viewed by 800
Abstract
The dynamics of vegetation changes and phenology serve as key indicators of interannual changes in vegetation productivity. Monitoring the changes in the Nanling grassland ecosystem using the remote sensing vegetation index is crucial for the rational development, utilization, and protection of these grassland [...] Read more.
The dynamics of vegetation changes and phenology serve as key indicators of interannual changes in vegetation productivity. Monitoring the changes in the Nanling grassland ecosystem using the remote sensing vegetation index is crucial for the rational development, utilization, and protection of these grassland resources. Grasslands in the hilly areas of southern China’s middle and low mountains have a high restoration efficiency due to the favorable combination of water and temperature conditions. However, the dynamic adaptation process of grassland restoration under the combined effects of climate change and human activities remains unclear. The aim of this study was to conduct continuous phenological monitoring of the Nanling grassland ecosystem, and evaluate its seasonal characteristics, trends, and the thresholds for grassland changes. The Normalized Difference Phenology Index (NDPI) values of Nanling Mountains’ grasslands from 2000 to 2021 was calculated using MOD09A1 images from the Google Earth Engine (GEE) platform. The Savitzky–Golay filter and Mann–Kendall test were applied for time series smoothing and trend analysis, and growing seasons were extracted annually using Seasonal Trend Decomposition and LOESS. A segmented regression method was then employed to detect the thresholds for grassland ecosystem restoration based on phenology and grassland cover percentage. The results showed that (1) the NDPI values increased significantly (p < 0.01) across all grassland patches, particularly in the southeast, with a notable rise from 2010 to 2014, and following an eastern to western to central trend mutation sequence. (2) the annual lower and upper NDPI thresholds of the grasslands were 0.005~0.167 and 0.572~0.727, which mainly occurred in January–March and June–September, respectively. (3) Most of the time series in the same periods showed increasing trends, with the growing season length varying from 188 to 247 days. (4) The overall potential productivity of the Nanling grassland improved. (5) The restoration of the mountain grasslands was significantly associated with the grassland coverage and mean NDPI values, with a key threshold identified at a mean NDPI value of 0.5 for 2.1% grassland coverage. This study indicates that to ensure the sustainable development and conservation of grassland ecosystems, targeted management strategies should be implemented, particularly in regions where human factors significantly influence grassland productivity fluctuations. Full article
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28 pages, 2179 KiB  
Article
Modeling Forest Regeneration Dynamics: Estimating Regeneration, Growth, and Mortality Rates in Lithuanian Forests
by Robertas Damaševičius and Rytis Maskeliūnas
Forests 2025, 16(2), 192; https://doi.org/10.3390/f16020192 - 21 Jan 2025
Viewed by 1064
Abstract
This study presents a novel approach to analyzing forest regeneration dynamics by integrating a Markov chain model with Multivariate Time Series (MTY) decomposition. The probabilistic tracking of age-class transitions was combined with the decomposition of regeneration rates into trend, seasonal, and irregular components, [...] Read more.
This study presents a novel approach to analyzing forest regeneration dynamics by integrating a Markov chain model with Multivariate Time Series (MTY) decomposition. The probabilistic tracking of age-class transitions was combined with the decomposition of regeneration rates into trend, seasonal, and irregular components, unlike traditional deterministic models, capturing the variability and uncertainties inherent in forest ecosystems, offering a more nuanced understanding of how Scots pine (Pinus sylvestris L.) and other tree species evolve under different management and climate scenarios. Using 20 years of empirical data from the Lithuanian National Forest Inventory, the study evaluates key growth and mortality parameters for Scots pine, Spruce (Picea abies), Birch (Betula pendula), and Aspen (Populus tremula). The model for Scots pine showed a 79.6% probability of advancing from the 1–10 age class to the 11–20 age class, with subsequent transitions of 82.9% and 84.1% for older age classes. The model for Birch shown a strong early growth rate, with an 84% chance of transitioning to the next age class, while the model for Aspen indicated strong slowdown after 31 years. The model indicated moderate early growth for Spruce with a high transition in later stages, highlighting its resilience in mature forest ecosystems. Sensitivity analysis revealed that while higher growth rates can prolong forest stand longevity, mortality rates above 0.33 severely compromise stand viability. The Hotelling T2 control chart identified critical deviations in forest dynamics, particularly in years 13 and 19, suggesting periods of environmental stress. The model offers actionable insights for sustainable forest management, emphasizing the importance of species-specific strategies, adaptive interventions, and the integration of climate change resilience into long-term forest planning. Full article
(This article belongs to the Special Issue Modeling Aboveground Forest Biomass: New Developments)
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17 pages, 1146 KiB  
Article
DFCNformer: A Transformer Framework for Non-Stationary Time-Series Forecasting Based on De-Stationary Fourier and Coefficient Network
by Yuxin Jin, Yuhan Mao and Genlang Chen
Information 2025, 16(1), 62; https://doi.org/10.3390/info16010062 - 17 Jan 2025
Viewed by 799
Abstract
Time-series data are widely applied in real-world scenarios, but the non-stationary nature of their statistical properties and joint distributions over time poses challenges for existing forecasting models. To tackle this challenge, this paper introduces a forecasting model called DFCNformer (De-stationary Fourier and Coefficient [...] Read more.
Time-series data are widely applied in real-world scenarios, but the non-stationary nature of their statistical properties and joint distributions over time poses challenges for existing forecasting models. To tackle this challenge, this paper introduces a forecasting model called DFCNformer (De-stationary Fourier and Coefficient Network Transformer), designed to mitigate accuracy degradation caused by non-stationarity in time-series data. The model initially employs a stabilization strategy to unify the statistical characteristics of the input time series, restoring their original features at the output to enhance predictability. Then, a time-series decomposition method splits the data into seasonal and trend components. For the seasonal component, a Transformer-based encoder–decoder architecture with De-stationary Fourier Attention (DSF Attention) captures temporal features, using differentiable attention weights to restore non-stationary information. For the trend component, a multilayer perceptron (MLP) is used for prediction, enhanced by a Dual Coefficient Network (Dual-CONET) that mitigates distributional shifts through learnable distribution coefficients. Ultimately, the forecasts of the seasonal and trend components are combined to generate the overall prediction. Experimental findings reveal that when the proposed model is tested on six public datasets, in comparison with five classic models it reduces the MSE by an average of 9.67%, with a maximum improvement of 40.23%. Full article
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