Dependence Structure Research Articles

Local Bootstrap for Network Data

SUMMARY In network analysis, we frequently need to conduct inference for network parameters based on one observed network. Since the sampling distribution of the statistic is often unknown, we need to rely on the bootstrap. However, due to the complex dependence structure among vertices, existing bootstrap methods often yield unsatisfactory performance, especially under small or moderate sample sizes. To this end, we propose a new network bootstrap procedure, termed local bootstrap, to estimate the standard errors of network statistics. We propose to resample the observed vertices along with their neighbor sets, and reconstruct the edges between the resampled vertices by drawing from the set of edges connecting their neighbor sets. We justify the proposed method theoretically with desirable asymptotic properties for statistics such as motif density, and demonstrate its excellent numerical performance in small and moderate sample sizes. Our method includes several existing methods, such as the empirical graphon bootstrap, as special cases. We investigate the advantages of the proposed methods over the existing methods through the lens of edge randomness, vertex heterogeneity, neighbor set size, which shed some light on the complex issue of network bootstrapping.

A framework for drought monitoring and assessment from a drought propagation perspective under non-stationary environments

According to the coupled influence of climate variation and anthropogenic activities, hydro-meteorological variables are hard to keep stationary in a changing environment. Consequently, the efficacy of traditional standardized drought indices, predicated upon the assumption of stationarity, has been called into question. In China, the challenge of drought monitoring and declaration is exacerbated by the need for multiple drought indices covering meteorological, agricultural, hydrological, and groundwater aspects, often lacking real-time availability. To address these challenges, we developed a framework for drought monitoring and assessment from a drought propagation perspective. Central to this is the Nonstationary Integrated Drought Index (NIDI), which integrates responses from meteorological, agricultural, hydrological, and groundwater droughts, accounting for climate change and anthropogenic influences. First, we analyse the process of drought propagation to select the suitable time scale standardized drought index. Subsequently, significant large-scale climatic indices are selected through linear and nonlinear correlation analyses to identify climate anomalies. Anthropogenic influences are assessed using indicators such as the Normalized Difference Vegetation Index (NDVI), Impervious Surface Ratio (ISR), and population density (POP). Nonstationary probability models are then developed for precipitation, soil moisture, runoff, and groundwater series, incorporating climatic and human-induced factors. Finally, the NIDI is calculated using a D-vine copula model, with parameter estimation and updating facilitated by a genetic algorithm, representing the temporal dependence structure among the variables. A case study in the Hulu River Basin of western China validated the NIDI. Results showed that the NIDI effectively accounts for nonstationary hydro-meteorological variables due to climate change and human activities, accurately reproducing their time-dependent structure. Compared to conventional indices like SPI, SSI, SRI, and SGI, the NIDI identifies more extreme drought events. In conclusion, the presented NIDI offers a more comprehensive approach to drought identification, providing valuable insights for accurate drought detection and effective drought-related policy-making.

Exploring the coherency and predictability between the stocks of artificial intelligence and energy corporations

This paper employs wavelet coherence, Cross-Quantilogram (CQ), and Time-Varying Parameter Vector-Autoregression (TVP-VAR) estimation strategies to investigate the dependence structure and connectedness between investments in artificial intelligence (AI) and eight different energy-focused sectors. We find significant evidence of dependence and connectedness between the stock returns of AI and those of the energy-focused sectors, especially during intermediate and long-term investment horizons. The relationship has become stronger since the COVID-19 pandemic. More specifically, results from the wavelet coherence approach show a stronger association between the stock returns of energy-focused sectors and AI, while results from the CQ analysis show that directional predictability from AI to energy-focused sectors varies across sectors, investment horizons, and market conditions. TVP-VAR results show that since the COVID-19 outbreak, AI has become more of a net shock receiver from the energy market. Our study offers crucial implications for investors and policymakers.

Estimation of marginal excess moments for Weibull-type distributions

AbstractWe consider the estimation of the marginal excess moment (MEM), which is defined for a random vector (X, Y) and a parameter $$\beta >0$$ β > 0 as $$\mathbb {E}[(X-Q_{X}(1-p))_{+}^{\beta }|Y> Q_{Y}(1-p)]$$ E [ ( X - Q X ( 1 - p ) ) + β | Y > Q Y ( 1 - p ) ] provided $$\mathbb {E}|X|^{\beta }< \infty $$ E | X | β < ∞ , and where $$y_{+}:=\max (0,y)$$ y + : = max ( 0 , y ) , $$Q_{X}$$ Q X and $$Q_{Y}$$ Q Y are the quantile functions of X and Y respectively, and $$p\in (0,1)$$ p ∈ ( 0 , 1 ) . Our interest is in the situation where the random variable X is of Weibull-type while the distribution of Y is kept general, the extreme dependence structure of (X, Y) converges to that of a bivariate extreme value distribution, and we let $$p \downarrow 0$$ p ↓ 0 as the sample size $$n \rightarrow \infty $$ n → ∞ . By using extreme value arguments we introduce an estimator for the marginal excess moment and we derive its limiting distribution. The finite sample properties of the proposed estimator are evaluated with a simulation study and the practical applicability is illustrated on a dataset of wave heights and wind speeds.

Multiple yield curve modeling and forecasting using deep learning

AbstractThis manuscript introduces deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets and exploit it to produce more accurate forecasts. By combining the self-attention mechanism and nonparametric quantile regression, our model generates both point and interval forecasts of future yields. The architecture is designed to avoid quantile crossing issues affecting multiple quantile regression models. Numerical experiments conducted on two different datasets confirm the effectiveness of our approach. Finally, we explore potential extensions and enhancements by incorporating deep ensemble methods and transfer learning mechanisms.

Sample selection bias in non-traditional lending: A copula-based approach for imbalanced data

Credit scoring models for non-traditional lending channels, such as peer-to-peer (P2P) lending platforms, are usually estimated only on the sample of accepted applicants. This may lead to biased estimates of the risk drivers. This issue can be addressed using a reject inference technique that includes the characteristics of rejected applicants in the model. Due to the low numbers of accepted applicants and default records, credit scoring models usually face a class imbalance problem. However, previous literature on sample selection models for credit scoring does not address the class imbalance issue. To fill this gap, we extend the Generalised Extreme Value (GEV) regression model for binary data to the sample selection framework. We consider the quantile function of the GEV distribution as a link function in both the selection and outcome equations. We use the copula function to model the dependence structure between the two equations for its flexibility. This proposal is called the Sample Selection Generalised Extreme Value (SSGEV) model and it is implemented in the R package BivGEV. We apply this model to a comprehensive dataset provided by Lending Club, and we show that parameter estimates obtained only on accepted P2P applicants are biased and coherently with the literature. The SSGEV model achieves a higher predictive accuracy than those obtained using univariate approaches or a sample selection probit model. Our proposal also provides more conservative estimates of the Value-at-Risk and the Expected Shortfall.

Rank-based correlation matrix estimation for high dimensional microbiome data

In recent years, the progress made in high-throughout sequencing techniques supports the analysis of microbial communities greatly. The fact that real-world microbiome data lie in a high-dimensional simplex makes conventional statistical analysis unreliable owing to the sum-to-one constraint. Motivated by the urgent requirements of directly inferring the dependence pattern and dependence intensity simultaneously among microbial taxa, we address the challenge of correlation matrix estimation for this kind of data. Assuming that the unobserved log-basis random vectors follow the elliptical distribution, a robust method built on the Kendall's tau statistic is developed to estimate the basis generalized correlation matrix. Regardless of the existence of the covariance, the basis generalized correlation matrix is always a reliable measure of dependence structure. Theoretically, we establish the convergence rate of the proposed estimator under the spectral norm. Support recovery is discussed as well. Empirically, simulation studies demonstrate the outstanding numerical performance of our method. We also apply our method to analyse a microbiome dataset from human gut. We provide all the codes at https://github.com/lwfwhunanhero/CRCE.

Giant spin seebeck effect with highly polarized spin current generation and piezoelectricity in flexible V2SeTeO altermagnet at room temperature

Studies on altermagnetic materials are attracting extensive research efforts owing to their directional dependent spin split band structure. However, it is rare to find reports on the possibility of multifunctionality in altermagnetic systems. Here, we explore the spin dependent transport properties and piezoelectricity of two-dimensional V2SeTeO altermagnet. The V2SeTeO system has a direct band gap of 0.32 eV with a Neel temperature of 510 K. We find a giant effective Seebeck coefficient of 0.64 mV/K at 300 K. This is several times larger than that found in bulk and other two-dimensional materials. Moreover, the effective Seebeck effect is entirely determined by either only spin-up or spin-down component. This feature implies that we can generate highly spin polarized current by temperature gradient at room temperature. We attribute this pure spin current generation to the directional dependent spin split band structure. Along with the spin dependent transport properties, we also find that the Janus V2SeTeO altermagnet shows outstanding flexibility and piezoelectric response with out-of-plane piezoelectric coefficient of d31=0.245pm/V. Overall, we propose that the V2SeTeO altermagnet system exhibits multifunctional physical properties at room temperature, and this can be utilized for potential spintronics and flexible piezoelectric applications simultaneously.

On learning sparse linear models from cross samples

The sample complexity of a sparse linear model where samples are dependent is studied in this paper. We consider a specific dependency structure of the samples which arises in some experimental designs such as drug sensitivity studies, where two sets of objects (drugs and cells) are sampled independently, and after crossing (making all possible combinations of drugs and cells), the resulting output (efficacy of drugs) is measured. We call these types of samples as “cross samples”. The dependency among such samples is strong, and existing theoretical studies are either inapplicable or fail to provide realistic bounds. We aim at analyzing the performance of the Lasso estimator where the underlying distributions are mixtures of Gaussians and the data dependency arises from the crossing procedure. Our theoretical results show that the performance of the Lasso estimator in case of cross samples follows that of the i.i.d. samples with differences in constant factors. Through numerical results, we observe a phase transition: When datasets are too small, the error for cross samples is much larger than for i.i.d. samples, but once the size is large enough, cross samples are nearly as useful as i.i.d. samples. Our theoretical analysis suggests that the transition threshold is governed by the level of sparsity of the true parameter vector being estimated.

Global evidence on the energy–environment dilemma: the role of energy-related uncertainty across diverse environmental indicators

ABSTRACT Several existing studies show that macroeconomic uncertainties intensify global environmental and climate challenges, putting the globe at risk of not being able to achieve the United Nations’ Sustainable Development Goals by 2030. In this study, we provide global evidence on the role of energy-related uncertainty in the energy – environment dilemma between 1996 and 2021. We employ three distinct environmental indicators – load capacity factor (LCF), carbon dioxide emissions (CO2), and ecological footprint (EFP) – alongside a comprehensive global energy-related uncertainty index and time-frequency-quantile methods based on the Wavelet Quantile Correlation, Cross-Quantilogram, and Wavelet Local Multiple Correlation with Dominance. The empirical results suggest negative and strong nonlinear dependencies between energy-related uncertainty and the LCF across periods and quantiles. The results further suggest that the energy-related uncertainty has positive and strong nonlinear dependences not only with CO2 emissions but also EFP across various periods and quantiles. The results further suggest that the dependences between energy-related uncertainty and environmental indicators vary across periods and quantiles, with evidence of stronger dependency structures in the long run. These findings underscore the substantial influence of energy-related uncertainties on contemporary environmental challenges. We suggest that governments and policymakers need to reshape policy directives toward mitigating the environmental effects of energy-related uncertainties.

Application of the Rosenblatt transformation in First-Order System Reliability approximations

The reliability assessment of structural systems presents a significant challenge in structural engineering. A commonly employed approximation is the First-Order System Reliability Method (FOSRM), which estimates system reliability using the FORM component reliabilities and sensitivity factors. An essential step in FORM involves transforming the random vector X into the standard vector U, often using the Rosenblatt transformation (RT). Several studies demonstrated that different conditioning orders in the RT yield different FORM component results. This study investigates how these differences on component level propagate into the FOSRM system level. We conducted several typical engineering case studies with various failure probabilities, system sizes, and dependency structures (Gaussian and Frank Copula). For the Frank Copula, different Rosenblatt conditioning orders systematically yielded different FOSRM results, with most cases showing differences between 10% and 30% in estimated failure probability. For some systems, these differences increased with system size, suggesting that greater variations might be observed for larger systems. Notably, systems with Gaussian Copula functions also proved vulnerable to the Rosenblatt conditioning order when different components were assessed with different conditioning orders. The observed differences were larger than previously reported and should be carefully considered in uniform safety assessments.

Bilayer period and ratio dependent structure and mechanical properties of TiN/MoN superlattices

Transition metal nitrides are widely used in the hard materials and protective coatings industry, but are limited by their low fracture toughness. Encouraged by previous studies on remarkable simultaneous improvements in strength and ductility through superlattice (SL) architectures, various TiN/MoN SL thin films were developed on MgO (100) substrates. By varying their bilayer periods (Λ) between 2 and 23 nm with bilayer ratios (Γ = ℓMoN:ℓTiN) of 0.5, 1, 2, and 2.7, their individual effects on structure and mechanical properties can be revealed. All SLs—independent of Λ, Γ, and nitrogen-to-metal (N/Me) ratio (within the analysed variations)—exhibit a rocksalt structure with high-order satellite peaks in X-ray diffraction. While the SLs with Γ = 2 have the lowest hardness (H)—presumably due to their overall lowest N/Me ratio—the SLs with Γ = 2.7 are the hardest with a neat superlattice effect. The SLs with Γ = 1 and 2.7 have a comparable superlattice effect on fracture toughness (KIC), peaking at Λ = 9.9 and 9.3 nm, respectively. Of all the SLs investigated, those with Γ = 1 provide the best blend of mechanical properties and dry sliding coefficient of friction (µ), such as H = 34.8±1.6 GPa, KIC = 4.1±0.2 MPa√m, and µ = 0.27 when Λ = 9.9 nm. Deepening current understanding of superlattice effects in general—particularly the influence of bilayer periods and ratios—in relation to the nitrogen supply and heterogeneous microstructures, our study accelerates the design of nanolayered coatings with desired structure-property combinations.

Modelling the VaR Using Integral Probability and Tail Dependence

In this paper, a method is proposed to estimate value at risk (VaR) in a multivariate context by employing the probability integral transformation (PIT) and tail dependence function to model extreme dependence structure. The proposed method involves two vectorial measures of VaR, which use either the distribution function or the survival function. Moreover, properties of these risk measures are analysed, and a connection between them and tail dependence functions is established.

Functional connectivity across the human subcortical auditory system using an autoregressive matrix-Gaussian copula graphical model approach with partial correlations.

The auditory system comprises multiple subcortical brain structures that process and refine incoming acoustic signals along the primary auditory pathway. Due to technical limitations of imaging small structures deep inside the brain, most of our knowledge of the subcortical auditory system is based on research in animal models using invasive methodologies. Advances in ultrahigh-field functional magnetic resonance imaging (fMRI) acquisition have enabled novel noninvasive investigations of the human auditory subcortex, including fundamental features of auditory representation such as tonotopy and periodotopy. However, functional connectivity across subcortical networks is still underexplored in humans, with ongoing development of related methods. Traditionally, functional connectivity is estimated from fMRI data with full correlation matrices. However, partial correlations reveal the relationship between two regions after removing the effects of all other regions, reflecting more direct connectivity. Partial correlation analysis is particularly promising in the ascending auditory system, where sensory information is passed in an obligatory manner, from nucleus to nucleus up the primary auditory pathway, providing redundant but also increasingly abstract representations of auditory stimuli. While most existing methods for learning conditional dependency structures based on partial correlations assume independently and identically Gaussian distributed data, fMRI data exhibit significant deviations from Gaussianity as well as high-temporal autocorrelation. In this paper, we developed an autoregressive matrix-Gaussian copula graphical model (ARMGCGM) approach to estimate the partial correlations and thereby infer the functional connectivity patterns within the auditory system while appropriately accounting for autocorrelations between successive fMRI scans. Our results show strong positive partial correlations between successive structures in the primary auditory pathway on each side (left and right), including between auditory midbrain and thalamus, and between primary and associative auditory cortex. These results are highly stable when splitting the data in halves according to the acquisition schemes and computing partial correlations separately for each half of the data, as well as across cross-validation folds. In contrast, full correlation-based analysis identified a rich network of interconnectivity that was not specific to adjacent nodes along the pathway. Overall, our results demonstrate that unique functional connectivity patterns along the auditory pathway are recoverable using novel connectivity approaches and that our connectivity methods are reliable across multiple acquisitions.

Asymptotic estimates for ruin probabilities in a bidimensional delay-claim risk model with subexponential claims

This article studies the asymptotic behaviors for some common ruin probabilities of a bidimensional delay-claim risk model, in which each claim follows a subexponential distribution and each claim-size inherits some dependence structure. Meanwhile, the asymptotic behavior for sum ruin probability of the bidimensional delay-claim risk model is investigated when the two components of each claim inter-arrival time vector are arbitrarily dependent.

Covariate-dependent spatio-temporal covariance models

Geostatistical regression models are widely used in environmental and geophysical sciences to characterize the mean and dependence structures for spatio-temporal data. Traditionally, these models account for covariates solely in the mean structure, neglecting their potential impact on the spatio-temporal covariance structure. This paper addresses a significant gap in the literature by proposing a novel covariate-dependent covariance model within the spatio-temporal random-effects model framework. Our approach integrates covariates into the covariance function through a Cholesky-type decomposition, ensuring compliance with the positive-definite condition. We employ maximum likelihood for parameter estimation, complemented by an efficient expectation conditional maximization algorithm. Simulation studies demonstrate the superior performance of our method compared to conventional techniques that ignore covariates in spatial covariances. We further apply our model to a PM2.5 dataset from Taiwan, highlighting wind speed’s pivotal role in influencing the spatio-temporal covariance structure. Additionally, we incorporate wind speed and sunshine duration into the covariance function for analyzing Taiwan ozone data, revealing a more intricate relationship between covariance and these meteorological variables.

(Invited) On Solar Seawater Splitting

We are currently witnessing the widest worldwide environmental disasters and it is now crucial for the future of humanity to transition to novel societies where environmental, energy, and economic policies are no longer based on endless-growth financial models and fossil fuel technologies to decrease our environmental footprint. The origin of this strong imbalance between human activities and the environment is found in the endless-growth economic systems in place in major countries worldwide as it inherently requires the use of endless cheap energy to be sustained, hence the massive use of coal and fossil fuels as energy sources for a more profitable energy return on energy invested, which might be good for the economy but not for our environment, health, and sustainable future. Technological innovations have always helped boost the economy numerous times throughout civilizations yet it must involve large-scale, clean, and cost-effective fabrication techniques and be based on efficient earth-abundant and easily recyclable materials. A transition to hydrogen-based energy and economy is ideal as it produces zero carbon emission and hydrogen fuel cell and forthcoming hydrogen combustion transportation are available worldwide. However, most of the hydrogen produced comes from nonrenewable sources, i.e. by steam reforming of methane which produces very large amount of carbon mono/dioxide. The most natural, cleanest and sustainable way to produce hydrogen at large scale is by solar seawater splitting[1]. Our strategy is to fabricate earth-abundant and non-toxic devices consisting of oriented arrays of quantum rods/dots of high purity synthesized by aqueous chemical growth at low temperature without surfactant and with controlled dimensionalities and surface chemistry[2] with intermediate bands for high visible-light conversion, band structure edges optimized for stability against photocorrosion and operation conditions at neutral pH, low bias and no sacrificial agent. Such characteristics, combined with the in-depth investigation of their size dependent and interfacial electronic structure[3] and electrical properties[4] provide better fundamental understanding and structure-efficiency relationships for a cost-effective and sustainable generation of hydrogen from the two most abundant and geographically-balanced free resources available, the sun and seawater. An overview of such a strategy is presented for oxides, nitrides, sulfides as well as semiconductor-molecular catalysts hybrids[5], their low-cost and large scale fabrication, physical characterization, photogenerated charge dynamics, dopant segregation and thermal processing effects[1].[1] K.C. Bedin et al J. Am. Ceram. Soc. 2023, 106, 79; I. Rodriguez-Gutierrez et al ECS J. Solid State Sci. Tech. 2022, 11, 043001; J. B. Souza Jr et al Appl. Phys. Lett. 2021, 119, 200501; Y. Chen et al J. Mater. Chem. C 2021, 9, 3726; A. Tofanello et al J. Appl. Phys. 2020, 128, 063103; APL Mater. 2020, 8, 040905; Y. Wei et al Sol. Energy Mater. Sol. Cells 2019, 201, 110083; X. Guan et al ACS Energy Lett. 2018, 3, 2230; J. Phys. Chem. C 2018, 122, 13797; J. Su et al J. Phys. Chem. Lett. 2017, 8, 5228; ACS Energy Lett. 2016, 1, 121; Y. Tachibana et al Nat. Photon. 2012, 6, 511; C.X. Kronawitter et al Energy Environ. Sci. 2011, 4, 3889[2] L.Vayssieres, Adv. Mater. 2003, 15, 464; Int. J. Nanotechnol. 2004 , 1, 1; Int. J. Nanotechnol. 2005, 2, 411; J. Phys. Chem. C 2009, 113, 4733; J. Lützenkirchen et al Colloids Interfaces 2020, 4, 39[3] L.Vayssieres et al Appl. Phys. Lett. 2011 99, 183101; Adv. Mater., 2005, 17, 2320; C.X. Kronawitter et al Phys. Rev. B 2012, 85, 125109; Energy Environ. Sci. 2014, 7, 3100; Nano Lett. 2011, 11, 3855; J. Phys. Chem. C 2012, 116, 22780; PhysChemChemPhys 2013, 15, 13483; M.G. Kibria et al Adv. Mater. 2016, 28, 8388; K. Nie et al Nano Energy 2018, 53, 493; C.L. Dong et al Chem. Eur. J. 2018, 24, 18356[4] J. Wang et al ACS Appl. Mater. Interfaces 2019, 11, 2031; J. Engel et al Adv. Func. Mater. 2014, 24, 4952; I. Rodriguez-Gutierrez et al Electrochim. Acta 2019, 308, 317; Appl. Phys. Lett. 2021, 119, 071602; K. C. Bedin et al Chin. J. Catal. 2022, 43, 1247[5] T. Benko et al Catal. Sci. Technol. 2021, 11, 6411; Y. Wei et al Nano Res. 2016, 9, 156

LLM-Assisted Data Augmentation for Chinese Dialogue-Level Dependency Parsing

Abstract Dialogue-level dependency parsing, despite its growing academic interest, often encounters underperformance issues due to resource shortages. A potential solution to this challenge is data augmentation. In recent years, large language models (LLMs) have demonstrated strong capabilities in generation, which can facilitate data augmentation greatly. In this study, we focus on Chinese dialogue-level dependency parsing, presenting three simple and effective strategies with LLM to augment the original training instances, namely word-level, syntax-level, and discourse-level augmentations, respectively. These strategies enable LLMs to either preserve or modify dependency structures, thereby assuring accuracy while increasing the diversity of instances at different levels. We conduct experiments on the benchmark dataset released by Jiang et al. (2023) to validate our approach. Results show that our method can greatly boost the parsing performance in various settings, particularly in dependencies among elementary discourse units. Lastly, we provide in-depth analysis to show the key points of our data augmentation strategies.

A dependent circular-linear model for multivariate biomechanical data: Ilizarov ring fixator study.

Biomechanical and orthopaedic studies frequently encounter complex datasets that encompass both circular and linear variables. In most cases (i) the circular and linear variables are considered in isolation with dependency between variables neglected and (ii) the cyclicity of the circular variables is disregarded resulting in erroneous decision making. Given the inherent characteristics of circular variables, it is imperative to adopt methods that integrate directional statistics to achieve precise modelling. This paper is motivated by the modelling of biomechanical data, that is, the fracture displacements, that is used as a measure in external fixator comparisons. We focus on a dataset, based on an Ilizarov ring fixator, comprising of six variables. A modelling framework applicable to the six-dimensional joint distribution of circular-linear data based on vine copulas is proposed. The pair-copula decomposition concept of vine copulas represents the dependence structure as a combination of circular-linear, circular-circular and linear-linear pairs modelled by their respective copulas. This framework allows us to assess the dependencies in the joint distribution as well as account for the cyclicity of the circular variables. Thus, a new approach for accurate modelling of mechanical behaviour for Ilizarov ring fixators and other data of this nature is imparted.

Air pollution prediction using blind source separation with Greylag Goose Optimization algorithm

Particularly, environmental pollution, such as air pollution, is still a significant issue of concern all over the world and thus requires the identification of good models for prediction to enable management. Blind Source Separation (BSS), Copula functions, and Long Short-Term Memory (LSTM) network integrated with the Greylag Goose Optimization (GGO) algorithm have been adopted in this research work to improve air pollution forecasting. The proposed model involves preprocessed data from the urban air quality monitoring dataset containing complete environmental and pollutant data. The application of Noise Reduction and Isolation techniques involves the use of methods such as Blind Source Separation (BSS). Using copula functions affords an even better estimate of the dependence structure between the variables. Both the BSS and Copula parameters are then estimated using GGO, which notably enhances the performance of these parameters. Finally, the air pollution levels are forecasted using a time series employing LSTM networks optimized by GGO. The results reveal that GGO-LSTM optimization exhibits the lowest mean squared error (MSE) compared to other optimization methods of the proposed model. The results underscore that certain aspects, such as noise reduction, dependence modeling and optimization of parameters, provide much insight into air quality. Hence, this integrated framework enables a proper approach to monitoring the environment by offering planners and policymakers information to help in articulating efficient environment air quality management strategies.