Search Results (34)

Addressing the challenge that, in real-world dynamic multi-objective optimization problems (DMOPs), the severity of changes between pareto optimal set (PS) varies at different times and exhibits nonlinear characteristics rather than simple translations or rotations—making them difficult for traditional prediction strategies to track accurately—this paper proposes a dynamic multi-objective optimization algorithm via trend-cycle decoupling and hybrid time-series prediction. The algorithm first applies the Hodrick-Prescott (HP) filter to decompose the time-series of historical PS centers into a smooth trend component and a fluctuating cycle component to cope with uncertainty in the severity of changes. Then, an AR(p) model is used to fit the trend sequence and infer the long-term linear direction of PS movement; a long short-term memory (LSTM) network learns the cycle sequence to capture nonlinear variation patterns. By fusing the two prediction results, the center of the PS in the new environment is located, and an initial population is constructed using a manifold-based population generation strategy. Comparative experiments on 13 standard dynamic test functions show that the proposed algorithm achieves an effective trade-off between prediction accuracy and computational cost and demonstrates strong robustness to complex time-varying environments. In particular, in scenarios where the pareto optimal front (PF) undergoes rotation, discontinuity, or time-varying shape (convexity/concavity) due to complex mappings in the decision space, the algorithm maintains notable tracking accuracy and population diversity by precisely capturing the PS evolution trajectory. Full article

The most widely used method for trend estimation in economics is the Hodrick-Prescott (HP) filter. The HP filter has various disadvantages, such as the arbitrary, frequency-dependent choice of the smoothing parameter λ, boundary problems, and difficult interpretation when linking to economic theory. We suggest an alternative method by improving some of these disadvantages using a data-driven, endogenous nonparametric trend estimation. A simulation study and different applications demonstrate the advantages of the nonparametric trend compared to the HP filter. We identify optimal time windows supporting the momentary growth trend. Within this window, economic fundamentals smoothly change and drive the trend. Full article

In the domain of river engineering, estimating the total sediment load in rivers is a crucial challenge. For tens to hundreds of kilometers downstream, the additional sand and gravel in the sediment can raise the elevation of channel beds. For highly braided rivers like the Brahmaputra-Jamuna, the accurate prediction of the total sediment load depends on the complex relationships among different hydro-meteorological variables. As a result, manual selection of the lagged features from only antecedent sediment records can produce suboptimal predictions, which can be considered a significant research gap. In addition, the predictive accuracy can be further enhanced through the application of advanced decomposition techniques. To address these deficiencies, we implemented three sophisticated feature selection methodologies: SelectKBest, Mutual Information, and Random Forest utilizing the Boruta Algorithm as an alternative to manual feature selection. Furthermore, we investigated complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), variational mode decomposition (VMD), and the Hodrick–Prescott Filter (HPF) to improve data mining efficiency. Four distinct artificial neural network (ANN) training algorithms were considered: back propagation (BP), cascade correlation (CC), conjugate gradient (CG), and Levenberg–Marquardt (LM), as alternatives to the conventional BP-based training approach. The effectiveness of the variants of the ANN was assessed in comparison to a powerful ensemble learning model, specifically the decision tree (DT). Results indicate that the HPF-enhanced ANN-LM model exhibited the strongest performance metrics when compared to alternative techniques, with values of NRMSE = 0.004, MAE = 455.242 kg/s, NSE = 0.998, and KGE = 0.990. The outcomes from Sobol’s sensitivity analysis suggest that the sediment dynamics in this region can be better predicted through the inclusion of rainfall-based features. Full article

The alpine grassland ecosystem in the Source Region of the Yellow River (SRYR) faces the dual pressures of ecological protection and economic development. Its ecological fragility and climate sensitivity make local animal husbandry susceptible to meteorological disasters. To overcome adverse selection and moral hazard in traditional animal husbandry insurance, this study integrates 963 field sampling observation data, over 400 valid herdsmen survey data, and long-term environmental time series variables. A random forest model (R² = 0.59, RMSE = 65.84 g/m², superior to the artificial neural network in this paper) was used to estimate grass yield. Hodrick–Prescott (HP) filtering was used to separate meteorological yield per unit area and derive yield loss rate. A joint distribution model of meteorological indicators and loss rate was constructed using a Copula function to capture tail-dependent structures, providing a basis for determining trigger thresholds and actuarial pricing of pure insurance premiums. The study reveals the transmission mechanism of climate disasters to feeding costs and designs regional drought and snow disaster index insurance. The compensation standard is based on meteorological indicators falling below the trigger threshold and a yield reduction rate greater than 5%. Using 10,000 Monte Carlo simulations, the drought premium rates for zones I-IV are determined to be 2.03–6.03%, and the snow premium rates to be 2.25–5.42%, corresponding to a premium of RMB 5.21–9.61 per mu for drought and RMB 5.78–8.64 per mu for snow. This design reduces basis risk through zoning and composite triggering, providing a scientific tool for climate risk management in alpine grasslands. Full article

This study examines how aggregate financial risk tolerance (FRT), measured from repeated survey responses, co-evolves with stock-market dynamics over time. The observed FRT index is treated as a noisy preference signal containing both gradual drift and episodic deviations, and its market relevance is evaluated under time variation, frequency components, and stress regimes. Using monthly data that align the survey-based FRT index with market returns and risk measures, a three-part econometric design is implemented. First, a time-varying parameter VAR (TVP-VAR) characterizes bidirectional, non-constant linkages between FRT and market outcomes. Second, signal-extraction methods decompose FRT into a smooth “normal” component and a high-frequency “abnormal” component (with robustness to alternative filters) to test whether short-run deviations contain distinct information for volatility and downside risk. Third, a Markov-switching specification assesses state dependence by testing whether the FRT–market relationship differs between low-stress and high-stress regimes. Across specifications, the FRT–market linkage is strongly state dependent: the sign and magnitude of FRT effects drift over time and differ across regimes, with high-frequency FRT deviations aligning more closely with risk dynamics than the smooth component. Predictive validation is provided via out-of-sample forecasting of next-month market risk using elastic net and gradient boosting relative to an AR(1) benchmark; explainability analysis (SHAP) indicates that abnormal FRT contributes incremental predictive content beyond standard market-state variables. Overall, the framework offers a mathematically transparent approach to modeling survey-based preference signals in markets and supports regime-aware forecasting and risk-management applications. Full article

The rise in seasonal lifestyle tourism, characterized by winter-escape health and wellness stays and long-term leisure residence, has intensified peak–off-peak imbalances and pressures on the allocation of tourism service supply in tropical island destinations. However, existing research lacks a systematic comparison of seasonal fluctuations and long-term evolution for this subgroup at the city/county level. Therefore, this study aims to characterize the seasonal pattern, long-term trend features, and typological differentiation of seasonal lifestyle tourism at the county level, and to compare differences across types. Using monthly data on seasonal lifestyle tourism for 18 cities/counties in Hainan from 2021 to 2024, we apply TRAMO/SEATS decomposition to identify seasonal structures and measure seasonal amplitude and employ the Hodrick–Prescott (HP) filter to extract trend components and determine their directions of change. We further construct five development types by integrating trend categories and changes in seasonal amplitude and test between-type differences using one-way analysis of variance (ANOVA). Results show that Hainan exhibits a stable “winter–spring peak and summer–autumn trough” pattern (peaks concentrated in January–March and December, with the off-season typically spanning May–October), with strong seasonality and pronounced spatial heterogeneity. The four-year mean seasonal range at the county level is 215.01, with high values clustered in southern Hainan; Haikou remains relatively low, while Wenchang shows an upward trend. Long-term trends are clearly differentiated: 13 counties show sustained growth, 2 show decline, and 3 display a U-shaped recovery (decline followed by rebound). Growth rates also vary substantially, with Qionghai increasing at roughly 27 times the rate of Qiongzhong. Integrating seasonal and trend characteristics yields five types, of which the Robust Development type accounts for the largest share (50%). Between-type differences are mainly reflected in tourism service supply capacity: the number of star-rated hotels (p = 0.033, η² = 0.530) and overnight visitors (p = 0.004, η² = 0.676) differ significantly across types, whereas differences in natural-environment conditions are not significant. This study provides a scientific basis for zoning management and optimizing low-season strategies in Hainan. Full article

Traditional approaches to predicting business cycles are limited by their omission of financial variables, which, in turn, leads to failures to signal financial-sector crises and to misestimate the duration and intensity of economic events. This study addresses this challenge by constructing a real-financial activity gap for South Africa and utilising it to predict the occurrence of economic recoveries. The study examines the period from 1970Q1 to 2023Q4, using real GDP, domestic credit, house prices, and share prices. The dynamic factor model and the Hodrick–Prescott filter are employed to construct the real-financial activity gap. The recursive ADF unit root test is used to assess the presence, frequency, and duration of economic recoveries. To validate the results, a Markov switching dynamic regression model is applied. The results reveal that the new gap tends to produce economic recovery predictions that are less frequent but longer in duration. In contrast, predictions based on real GDP lead to more frequent but shorter recoveries. The new gap suggests that financial variables contribute to stabilising growth over extended periods, whereas real GDP reflects quicker but more volatile economic adjustments. The latest gap offers a more stable basis for forecasting recoveries, aiding policymakers in better anticipating and mitigating economic downturns. Accordingly, the output gap and the real-financial activity gap should be used as complements. Full article

This study analyzes the evolution of the Mexico–U.S. trade balance as a seasonally adjusted time series, comparing the Hodrick–Prescott (HP) filter and wavelet analysis. The HP filter allowed the trend and cycle to be extracted from the series, while wavelets decomposed the information into different time scales, revealing short-, medium-, and long-term fluctuations. The results show that HP provides a simplified view of the trend, while wavelets more accurately capture key events and cyclical dynamics. It is concluded that wavelets offer a more robust tool for studying the volatility and persistence of economic shocks in bilateral trade. Full article

This study examines the synchronization of economic and growth cycles between China and the United States of America amid ongoing economic and geopolitical tensions. Using a Markov-Switching–Vector Autoregression (MS-VAR) model, the analysis applies the Hodrick–Prescott and Baxter–King filters to monthly data from January 2000 to December 2024, capturing trends and cyclical fluctuations. The findings reveal asymmetries in economic synchronization, with differences in recession and expansion durations influenced by trade disputes, financial integration, and external shocks. As the rivalry between the two nations intensifies, marked by trade wars, technological competition, and geopolitical conflicts, understanding their economic co-movement becomes crucial. This study contributes to the literature by providing empirical insights into their evolving interdependence and offers policy recommendations for mitigating asymmetric shocks and promoting global economic stability. Full article

With the rapid development of the Internet, the speed and scope of sudden public events disseminating in cyberspace have grown significantly. Current methods of quantifying public opinion heat often neglect emotion-driven factors and user interaction behaviors, making it difficult to accurately capture fluctuations during dissemination. To address these issues, first, this study addressed the complexity of interaction behaviors by introducing an approach that employs the information gain ratio as a weighting indicator to measure the “interaction heat” contributed by different interaction attributes during event evolution. Second, this study built on SnowNLP and expanded textual features to conduct in-depth sentiment mining of large-scale opinion texts, defining the variance of netizens’ emotional tendencies as an indicator of emotional fluctuations, thereby capturing “emotional heat”. We then integrated interactive behavior and emotional conflict assessment to achieve comprehensive heat index to quantification and dynamic evolution analysis of online public opinion heat. Subsequently, we used Hodrick–Prescott filter to separate long-term trends and short-term fluctuations, extract six key quantitative features (number of peaks, time of first peak, maximum amplitude, decay time, peak emotional conflict, and overall duration), and applied K-means clustering algorithm (K-means) to classify events into three propagation patterns, which are extreme burst, normal burst, and long-tail. Finally, this study conducted ablation experiments on critical external intervention nodes to quantify the distinct contribution of each intervention to the propagation trend by observing changes in the model’s goodness-of-fit ($R^2$) after removing different interventions. Through an empirical analysis of six representative public opinion events from 2024, this study verified the effectiveness of the proposed framework and uncovered critical characteristics of opinion dissemination, including explosiveness versus persistence, multi-round dissemination with recurring emotional fluctuations, and the interplay of multiple driving factors. Full article

The modelling of the trend component of economic time series has a long history, and the most primitive and popular model displays the trend as a linear function of time. However, the residuals of such a linear trend frequently exhibit long-period fluctuations. The Hodrick–Prescott (HP) filter is able to capture such long-period fluctuations well, resulting in a very realistic trend-cycle decomposition. It may be queried whether the HP trend residuals no longer contain useful long-period fluctuations. If such long-period fluctuations are present, then taking them into consideration could improve the HP trend. In a recent article, a new approach to address this issue, the boosted HP (bHP) filter, was proposed. The three trends mentioned above, i.e., the linear trend, the HP trend, and the bHP trend, can be treated in a unified manner. In this paper, we demonstrate the relationship in detail. We show how the bHP trend is constructed from the linear/HP trend, and long-period fluctuations remained in their trend residuals. Full article

With the increasing complexity of the power system and the increasing load volatility, accurate load forecasting plays a vital role in ensuring the safety of power supply, optimizing scheduling decisions and resource allocation. However, the traditional single model has limitations in extracting the multi-frequency features of load data and processing components with varying complexity. Therefore, this paper proposes a complementary forecasting method based on bi-level decomposition and complexity analysis. In the paper, Pyraformer is used as a complementary model for the Single Channel Enhanced Periodicity Decoupling Framework (SCEPDF). Firstly, a Hodrick Prescott Filter (HP Filter) is used to decompose the electricity data, extracting the trend and periodic components. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is used to further decompose the periodic components to obtain several IMF components. Secondly, based on the sample entropy, spectral entropy, and Lempel–Ziv complexity, a complexity evaluation index system is constructed to comprehensively analyze the complexity of each IMF component. Then, based on the comprehensive complexity of each IMF component, different components are fed into the complementary model. The predicted values of each component are combined to obtain the final result. Finally, the proposed method is tested on the quarterly electrical load dataset. The effectiveness of the proposed method is verified through comparative and ablation experiments. The experimental results show that the proposed method demonstrates excellent performance in short-term electricity load forecasting tasks. Full article

Groundwater serves as an indispensable global resource, essential for agriculture, industry, and the urban water supply. Predicting the groundwater level in karst regions presents notable challenges due to the intricate geological structures and fluctuating climatic conditions. This study examines Qingzhen City, China, introducing an innovative hybrid model, the Hodrick–Prescott (HP) filter–Long Short-Term Memory (LSTM) network (HP-LSTM), which integrates the HP filter with the LSTM network to enhance the precision of groundwater level forecasting. By attenuating short-term noise, the HP-LSTM model improves the long-term trend prediction accuracy. Findings reveal that the HP-LSTM model significantly outperformed the conventional LSTM, attaining R² values of 0.99, 0.96, and 0.98 on the training, validation, and test datasets, respectively, in contrast to LSTM values of 0.92, 0.76, and 0.95. The HP-LSTM model achieved an RMSE of 0.0276 and a MAPE of 2.92% on the test set, significantly outperforming the LSTM model (RMSE: 0.1149; MAPE: 9.14%) in capturing long-term patterns and reducing short-term fluctuations. While the LSTM model is effective at modeling short-term dynamics, it is more prone to noise, resulting in greater prediction errors. Overall, the HP-LSTM model demonstrates superior robustness for long-term groundwater level prediction, whereas the LSTM model may be better suited for scenarios requiring rapid adaptation to short-term variations. Selecting an appropriate model tailored to specific predictive needs can thus optimize groundwater management strategies. Full article

The Whittaker–Henderson (WH) graduation is a smoothing method for equally spaced one-dimensional data such as time series. It includes the Bohlmann filter, the Hodrick–Prescott (HP) filter, and the Whittaker graduation as special cases. Among them, the HP filter is the most prominent trend-cycle decomposition method for macroeconomic time series such as real gross domestic product. Recently, a modification of the HP filter, the boosted HP (bHP) filter, has been developed, and several studies have been conducted. The basic idea of the modification is to achieve more desirable smoothing by extracting long-term fluctuations remaining in the smoothing residuals. Inspired by the modification, this paper develops the boosted version of the WH graduation, which includes the bHP filter as a special case. Then, we establish its properties that are fundamental for applied work. To investigate the properties, we use a spectral decomposition of the penalty matrix of the WH graduation Full article

Predicting the concentration of dissolved gases in transformer oil is a critical activity for the early detection of potential faults. To address the prevalent issue of data leakage in current prediction methods, this paper proposes a prediction method that completely avoids data leakage. First, the Hodrick Prescott (HP) filter is used for stepwise decomposition to obtain the long-term trend and high-frequency periodic component. The high-frequency periodic component is further decomposed using singular spectrum analysis (SSA) to extract periodic features. Dispersion entropy (DE) and fuzzy entropy (FE) are utilized alongside the HP and SSA methods to determine the optimal decomposition windows during the process, enhancing the ability of the model to acquire time series features. Then, variational mode decomposition (VMD) is applied to remove noise from the high-frequency component. Finally, the long short-term memory network (LSTM) is employed to predict each decomposed component, and the network parameters undergo optimization through the sparrow search optimization algorithm (SSOA). The two case studies in this work verify that the proposed model excels over other prediction means, providing strong support for subsequent fault prediction. Full article