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There are growing concerns for reserves estimation of Incurred But Not Reported (IBNR) claims in actuarial sciences. In this paper, we propose a copula-based dependency model to capture the relationship between two main IBNR reserve variables, i.e., the "time between two successive occurrences" and "delay time". A maximum likelihood estimation method is used to estimate the parameters of the model. A simulation study is conducted to evaluate the validity of the theoretical results. Moreover, the proposed method is applied to predict the number of claims for the next years of a portfolio from a major automobile insurer and is compared to the classical Chain-Ladder (CL) model forecasting. [ABSTRACT FROM AUTHOR]

In this paper, we present the concept of being monotonic in sequence according to a specific direction for a collection of random variables. This concept broadens the existing notions of multivariate dependence, such as sequential left-tail and right-tail dependence. Furthermore, we explore connections with other multivariate dependence concepts, highlight key properties, and analyze the new concept within the framework of copulas. Several examples are provided to demonstrate our findings. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach to estimate tail dependence in financial contagion using mixture copulas. Addressing the challenges of weight parameter estimation in conventional models, we propose a Bayesian model averaging method to determine optimal copula weights. Through both simulations and empirical studies, the proposed method demonstrates improved robustness and accuracy, particularly when handling extreme weight scenarios. These advancements offer more reliable measurements of financial contagion, contributing to enhanced risk management and policy-making in interconnected financial markets. [ABSTRACT FROM AUTHOR]

Word embeddings are a fundamental tool in natural language processing. Currently, word embedding methods are evaluated on the basis of empirical performance on benchmark data sets, and there is a lack of rigorous understanding of their theoretical properties. This paper studies word embeddings from a statistical theoretical perspective, which is essential for formal inference and uncertainty quantification. We propose a copula-based statistical model for text data and show that under this model, the now-classical Word2Vec method can be interpreted as a statistical estimation method for estimating the theoretical pointwise mutual information (PMI). We further illustrate the utility of this statistical model by using it to develop a missing value-based estimator as a statistically tractable and interpretable alternative to the Word2Vec approach. The estimation error of this estimator is comparable to Word2Vec and improves upon the truncation-based method proposed by Levy and Goldberg (Adv. Neural Inf. Process. Syst., 27, 2177–2185 2014). The resulting estimator also is comparable to Word2Vec in a benchmark sentiment analysis task on the IMDb Movie Reviews data set and a part-of-speech tagging task on the OntoNotes data set. [ABSTRACT FROM AUTHOR]

This paper aims to develop a method to construct an asymmetric copula, based on which a closed form of the cumulative bivariate failure rate can be obtained. The construction method differs from existing ones. This new method can facilitate the derivation of some results such as the estimation of the expected number of occurrences for a system whose failure process is modelled by a bivariate stochastic process or the expected cost in optimisation of maintenance policies. [ABSTRACT FROM AUTHOR]

The research focuses on the reliability analysis of a complex system comprising two interconnected subsystems. Each subsystem consists of three identical units arranged in parallel. The operational policy employed is the 1-out-of-3: G policy, which means that as long as at least one unit is operational in each subsystem, the system as a whole remains functional. The failure rates of the units within the subsystems are consistent and follow an exponential distribution. To address unit failures and repair them, the Gumbel-Hougaard copula repair method is employed. The research investigates various reliability metrics, including system availability, system reliability, mean time to failure (MTTF), and sensitivity analysis. The researchers employ stochastic theory, differential equations, and supplementary variables to model and analyze the reliability behavior of the system. Moreover, the model's findings can guide decision-making processes related to system design, component selection, and maintenance strategies. System engineers and managers can utilize the insights gained from the reliability analysis to optimize the system's performance, enhance its reliability, and reduce costs associated with maintenance and repair. [ABSTRACT FROM AUTHOR]

In this research, we are concerned with intraday volatilities computed by functional ARCH(1) (fARCH(1), for short) model for high-frequency financial time series. A conditional-Copula multiple change point detection (CPD) for intraday volatilities is proposed using fARCH(1), bivariate Gaussian Copula and t-Copula conditional distributions. We employ current available multivariate CPD models which include energy test based control chart (ETCC) and nonparametric multivariate change point model (NPMVCP) to implement the proposed CPD method for the intraday volatilities. A simulation study is conducted to demonstrate that the functional ARCH based conditional-Copula CPD for the intraday volatilities can be a useful econometrics method to detect abnormal intraday volatilities in the financial market. We analyze intraday volatilities of the Korea composite stock price index (KOSPI) and the Hyundai-Motor (HDM) company stock data with one minute high-frequency to illustrate our proposed CPD method. [ABSTRACT FROM AUTHOR]

Estimation of the uncertainties of geotechnical parameters is a fundamental task in slope reliability analysis, and it becomes more challenging when only limited data on geotechnical parameters are available. In this study, a Bayesian bootstrap-Copula coupled method is proposed for slope reliability analysis based on limited geotechnical data. Specifically, the bivariate distribution of shear strength parameters ((cohesion (c) and friction angle (φ)) can be evaluated using the Bayesian bootstrap method and Copula theory, and then the slope reliability can be calculated using Monte Carlo simulation (MCS). Application to a homogeneous, undrained cohesive slope demonstrates the accuracy and effectiveness of the proposed approach. The results indicate that even when data are limited, the bivariate distribution of c and φ can be determined and the estimated statistics met the predefined ones well. Satisfying estimations of the mean ( μ FS ) and standard deviation ( σ FS ) of the factor of safety (FS) and failure probability (Pf) can be obtained. The representative sliding surface with the greatest likelihood is found to approximate the critical one based on the mean values of c and φ. Besides, when the available sample size of geotechnical data exceeds a threshold, stable estimations of the bivariate distribution of c and φ can be obtained, and the estimated μ FS is stable, while the values of σ FS and Pf synchronously vary within a small range. Applications of the proposed Bayesian bootstrap-Copula coupled method indicate that it can be used to estimate the bivariate distribution of correlated parameters and the reliability of various geotechnical problems based on limited data. [ABSTRACT FROM AUTHOR]

In observational/field studies, competing risks and left-truncation may co-exist, yielding 'left-truncated competing risks' settings. Under the assumption of independent competing risks, parametric estimation methods were developed for left-truncated competing risks data. However, competing risks may be dependent in real applications. In this paper, we propose a Bayesian estimator for both independent competing risks and copula-based dependent competing risks models under left-truncation. The simulations show that the Bayesian estimator for the copula-based dependent risks model yields the desired performance when competing risks are dependent. We also comprehensively explore the choice of the prior distributions (Gamma, Inverse-Gamma, Uniform, half Normal and half Cauchy) and hyperparameters via simulations. Finally, two real datasets are analyzed to demonstrate the proposed estimators. [ABSTRACT FROM AUTHOR]

In many cases, ensemble weather forecasts produced by numerical weather prediction (NWP) models exhibit systematic bias and under-dispersion. Over the past two decades, various ensemble postprocessing approaches have been developed to address this issue. These approaches include classical methods such as ensemble model output statistics (EMOS), Bayesian model averaging (BMA), and advanced machine learning-based approaches. In most ensemble post-processing approaches, it is implicitly assumed that there is statistical independence between different forecast margins, such as lead time, location, and meteorological variables. However, this assumption is not valid for realistic forecast application scenarios. End users may be interested in scenarios such as total hydrological basin precipitation, temporal evolution of precipitation, or the interaction of precipitation and temperature, especially when temperatures are close to zero degrees Celsius. Important examples include hydrological applications, air traffic management, and energy forecasting. Such dependencies exist in raw ensemble forecasts, but these dependencies are ignored if standard univariate post-processing methods are applied separately to each margin. In recent years, various multivariate post-processing methods have been proposed. These methods can be categorized into two approaches. The goal of the first approach is to directly model the joint distribution by fitting a specific multivariate probability distribution. This approach is mainly used in low-dimensional problems or when a specific structure is chosen for the application at hand. For example, multivariate models for temperature across space, for wind vectors, and joint models for temperature and wind speed. The second approach is a two-step approach. In the first step, univariate post-processing methods are applied independently to all dimensions, and samples are generated from the resulting probability distributions. In the second step, the multivariate dependencies are recovered by reordering the univariate sample values according to the ranking order structure of a specific multivariate dependence pattern. Mathematically, this is equivalent to using a copula (parametric or nonparametric). Examples include ensemble copula coupling (ECC), Schaake Shuffle, and the Gaussian copula approach. This paper presents multivariate ensemble post-processing of temperature, two meter above ground using the ECC approach. The EMOS method is used for univariate post-processing. The performance of the raw ensemble, EMOS post-processed ensemble, and ECC systems is evaluated using energy score (ES) and variogram score (VS). The ECMWF 51-member ensemble system is used as raw data for the period from January 1, 2018 to December 31, 2023. The results showed that in addition to eliminating the bias of the raw ensemble forecast, the ECC method also preserved the dependence structure between the ensemble members. In contrast, the EMOS method only eliminated the biases without considering the dependence between the ensemble members. Because of its ability to preserve the dependence structure, the ECC method was able to achieve significantly better results than the EMOS method on a variety of metrics, including energy scores and variogram score. This suggests that the ECC method is a valuable tool for ensemble post-processing, and that it should be considered for a wide range of applications. [ABSTRACT FROM AUTHOR]

We estimate conditional value-at-risk (CoVaR) for stock and currency markets under different market statuses and then apply them to study the asymmetry of risk spillovers between currency and stock markets under different market statuses. Empirical results show that risk spillovers between different statuses in stock and currency markets are significant and asymmetric. Next, for most countries, the scale and volatility of CoVaR are more prominent when return-chasing effects, rather than portfolio rebalancing effects, dominate. Finally, when stock prices in major industrial countries fall sharply or currencies depreciate significantly, investing in Japanese stocks is relatively safe for U.S. investors. [ABSTRACT FROM AUTHOR]

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example. [ABSTRACT FROM AUTHOR]

The measurement of economic contribution of tourism in a given geographical area needs, besides non-monetary measures such frequentation ones, a monetary one namely tourism expenditure. In addition to these macroeconomic related purposes, the whole statistical tourism measures shed light on tourist behavior, which are of great interest for marketing analysis. This study proposes to model the joint distribution of tourism expenditure disaggregated by category simultaneously with a set of covariates associated with the tourist's trip (including destination, days of stay, season of the year, among others). The dependence structure, among all variables, is established by a family of pairwise copulas (regular vines), which allows fitting a high-dimensional multivariate statistical model. As an application, the model is calibrated with a database for the Fribourg region (Switzerland). The good fit of the model to the data is observed both in the marginal distributions and in the dependence structure. The parameters representing dependence of the vine copula show strong relationship between the different categories of spending, both for tourists and excursionists. The empirical results show that the key variables to understand the associations between them are the destination in the region and the place of origin of the visitor. In general terms, the empirical results show that a visitor that expends more on one item is likely to expend more on a complementary items of spending. [ABSTRACT FROM AUTHOR]

The growing interest in cryptocurrencies has brought this new means of exchange to the attention of the financial world. This study aims to investigate the effects that a cryptocurrency can have when it is considered as a financial asset. The analysis is carried out from an ex‐post perspective, evaluating the performance achieved in a certain period by three different portfolios. These are the one composed only of equities, bonds and commodities, the second one only of cryptocurrencies, and the third one is a combination of these both ones and thus made up of all considered "traditional" assets and the most performing cryptocurrency of the second portfolio. For these purposes, the classic variance‐covariance approach is applied where the calculation of the risk structure is done via the GARCH‐Copula and GARCH‐Vine Copula approaches. The optimal weights of the assets in the optimized portfolios are determined through Markowitz optimization problem. The analysis mainly showed that the portfolio composed of cryptocurrency and traditional assets has a higher Sharpe index, from an ex‐post perspective, and more stable performances, from an ex‐ante perspective. We justify our selection of the Markowitz approach over conditional VaR and expected shortfall due to their heightened sensitivity to unsystematic extreme events in crypto markets. [ABSTRACT FROM AUTHOR]

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm. [ABSTRACT FROM AUTHOR]

A common problem in clinical trials is to test whether the effect of an explanatory variable on a response of interest is similar between two groups, for example, patient or treatment groups. In this regard, similarity is defined as equivalence up to a pre-specified threshold that denotes an acceptable deviation between the two groups. This issue is typically tackled by assessing if the explanatory variable's effect on the response is similar. This assessment is based on, for example, confidence intervals of differences or a suitable distance between two parametric regression models. Typically, these approaches build on the assumption of a univariate continuous or binary outcome variable. However, multivariate outcomes, especially beyond the case of bivariate binary responses, remain underexplored. This paper introduces an approach based on a generalized joint regression framework exploiting the Gaussian copula. Compared to existing methods, our approach accommodates various outcome variable scales, such as continuous, binary, categorical, and ordinal, including mixed outcomes in multi-dimensional spaces. We demonstrate the validity of this approach through a simulation study and an efficacy-toxicity case study, hence highlighting its practical relevance. [ABSTRACT FROM AUTHOR]

The study investigates the nonlinear contagion, tail dependence, and Granger causality relations with TAR-TR-GARCH–copula causality methods for daily Bitcoin, Fintech, energy consumption, and CO2 emissions in addition to examining these series for entropy, long-range dependence, fractionality, complexity, chaos, and nonlinearity with a dataset spanning from 25 June 2012 to 22 June 2024. Empirical results from Shannon, Rényi, and Tsallis entropy measures; Kolmogorov–Sinai complexity; Hurst–Mandelbrot and Lo's R/S tests; and Phillips' and Geweke and Porter-Hudak's fractionality tests confirm the presence of entropy, complexity, fractionality, and long-range dependence. Further, the largest Lyapunov exponents and Hurst exponents confirm chaos across all series. The BDS test confirms nonlinearity, and ARCH-type heteroskedasticity test results support the basis for the use of novel TAR-TR-GARCH–copula causality. The model estimation results indicate moderate to strong levels of positive and asymmetric tail dependence and contagion under distinct regimes. The novel method captures nonlinear causality dynamics from Bitcoin and Fintech to energy consumption and CO2 emissions as well as causality from energy consumption to CO2 emissions and bidirectional feedback between Bitcoin and Fintech. These findings underscore the need to take the chaotic and complex dynamics seriously in policy and decision formulation and the necessity of eco-friendly technologies for Bitcoin and Fintech. [ABSTRACT FROM AUTHOR]

In this article, I propose a method to estimate the counterfactual distribution of an outcome variable when the treatment is endogenous, continuous, and its effect is heterogeneous. The types of counterfactuals considered are those in which the change in treatment intensity can be correlated with the individual effects or when some of the structural functions are changed by some other group's counterparts. I characterize the outcome and the treatment with a triangular system of equations in which the unobservables are related by a copula that captures the endogeneity of the treatment, which is nonparametrically identified by inverting the quantile processes that determine the outcome and the treatment. Both processes are estimated using existing quantile regression methods, and I propose a parametric and a nonparametric estimator of the copula. To illustrate these methods, I estimate several counterfactual distributions of the birth weight of children, had their mothers smoked differently during pregnancy. [ABSTRACT FROM AUTHOR]

Asur / Asuri is a North Munda language of the Kherwarian branch; a sister language to Mundari and Ho. The Munda verb morphology in general and especially the tense and aspect marking on verbs have been complex and hard to analyze; this is also the case with the Asur language. The study is a preliminary investigation into the verb morphology of the Asur language. Asur language has remained largely undocumented and undescribed by documentary linguistics and therefore, the study along with analysis of verb morphology also provides primary data. It attempts to delve into the complex tense-aspect encoding system of Asur verbs and the need to consider the presence and absence of transitivity markers -n and -d̪ alongside tenseaspect markers. Within the scope of the study, tense aspect encoding, passivation, narrativization, reciprocal marking, serial verb construction, copula and auxiliary in the Asur language have been investigated. [ABSTRACT FROM AUTHOR]

Credit Valuation Adjustment is a balance sheet item which is nowadays subject to active risk management by specialized traders. However, the most important risk factors, which are the default intensities of the counterparties, affect in a nondifferentiable way the most general Monte Carlo estimator of the adjustment, through simulation of default times. Thus the computation of first- and second-order (pure and mixed) sensitivities with respect to inputs affecting these risk factors cannot rely on direct path-wise differentiation, while any approach involving finite differences is slow and shows very high statistical noise. We present ad hoc estimators which have empirically a much smaller variance while offering very low runtime overheads over the baseline computation of the price adjustment, regardless of the number of sensitivities of interest, by leveraging adjoint (i.e., backward) algorithmic differentiation in their implementation. These estimators allow for a generic copula-based dependence structure among the default events, and can be applied beyond our main application, to payoffs depending on more than two of them. We also discuss the conversion of the so-obtained sensitivities to model parameters (e.g., default intensities) into sensitivities to the market quotes used in calibration (e.g., Credit Default Swap spreads) by generalizations of an existing implicit-function based first-order algorithm. [ABSTRACT FROM AUTHOR]

Using Induced Order Statistics to Construct Optimal Impact Portfolios with General Dependence and Marginals We develop a mathematical framework for constructing optimal impact portfolios and quantifying their financial performance by characterizing the returns of impact-ranked assets using induced order statistics and copulas. Our results apply to any joint distribution of impact factors and residual returns, making them broadly applicable to a wide range of contexts. We develop significant extensions of the theory of induced order statistics, with which we are able to characterize the distribution of residual returns of individual assets ranked by the impact factor. Our framework provides a toolkit for practitioners to construct impact portfolios and quantify their performance based on real data. This allows impact investors to achieve higher risk-adjusted returns than those with impact portfolios constructed using simpler heuristics such as negative or positive screening. We develop a mathematical framework for constructing optimal impact portfolios and quantifying their financial performance by characterizing the returns of impact-ranked assets using induced order statistics and copulas. The distribution of induced order statistics can be represented by a mixture of order statistics and uniformly distributed random variables, where the mixture function is determined by the dependence structure between residual returns and impact factors—characterized by copulas—and the marginal distribution of residual returns. This representation theorem allows us to explicitly and efficiently compute optimal portfolio weights under any copula. This framework provides a systematic approach for constructing and quantifying the performance of optimal impact portfolios with arbitrary dependence structures and return distributions. Funding: Research funding from the China National Key R&D Program [Grant 2022YFA1007900], the China National Natural Science Foundation [Grants 12271013, 72342004], the Fundamental Research Funds for the Central Universities (Peking University), and the MIT Laboratory for Financial Engineering is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.0400. [ABSTRACT FROM AUTHOR]

We introduce a clustering method for time series based on tail dependence. Such a method also considers spatial constraints by means of a suitable procedure merging temporal and spatial dependence via extreme-value copulas. The cluster composition depends on the choice of the hyper-parameter α ∈ (0 , 1) used to calibrate the contribution of the spatial dependence to the overall dissimilarity. A novel heuristic approach to select α based on a suitable connectedness index associated to each cluster of the partition is proposed. [ABSTRACT FROM AUTHOR]

Drought is a global threat caused by the persistent challenges of climate change. It is important to identify drought conditions based on weather variables and their patterns. In this study, we enhanced the Standardized Precipitation Index (SPI) by integrating ground temperature data to develop a more comprehensive metric for evaluating drought severity: the Multivariate Standardized Drought Index. Our metric offers a dual assessment of drought severity, taking into account both the intensity of the drought and its duration. We employ this evaluation in a primary paddy cultivation region of Sri Lanka, with the aim of shedding light on the prevailing drought conditions affecting paddy crops due to insufficient water supply and prolonged periods of elevated temperatures. Additionally, we calibrate our metric by aligning it with historical drought records and subsequently compare the outcomes with those derived from the conventional SPI. [ABSTRACT FROM AUTHOR]

Random weighted k$$ k $$‐out‐of‐n$$ n $$ systems are very useful in modeling the lifetimes of systems, wherein the success or failure of a system depends not only on its current operational status, but also on the contributions made by its components. In this paper, we consider random weighted k$$ k $$‐out‐of‐n$$ n $$ systems with redundant components drawn randomly from a mixed population consisting of m$$ m $$ different subpopulations/substocks. We study different optimal allocation policies of active redundancies and minimal repair components in a random weighted k$$ k $$‐out‐of‐n$$ n $$ system. Moreover, we investigate how the heterogeneity of subpopulations of items impacts the lifetime of a random weighted k$$ k $$‐out‐of‐n$$ n $$ system. We also present some simulational results and a real data analysis for illustrative purpose. [ABSTRACT FROM AUTHOR]

Drought events are a major cause of large crop yield losses with implications for food security and farmers' incomes. Growing multiple crops simultaneously during a cropping season is a well‐known on‐farm risk management strategy to cope with these drought risks. However, the effectiveness of this crop diversification under different severity levels of drought and how this effectiveness is influenced by the crop composition is unclear. This article provides new methodological and empirical insights to assess the effectiveness of such diversification, in particular to cope with extreme drought. We apply and evaluate nested Archimedean copulas and elliptical copulas to assess simultaneous farm‐level yield losses of different cash crops in German agriculture (winter wheat, winter barley, winter rapeseed, sugar beet, and grain maize) under different drought severity levels (N = 249,756; regionally pooled farm‐level crop‐yield pairs, 1995–2019). We show that on‐farm crop diversification contributes to cope with drought risks, but its effectiveness varies considerably across regions, crop pairs, and drought severity. Our results underline that cropping system diversification alone is often not sufficient to cope with drought risks, but that the right crop combinations are needed. For example, during a severe drought (one in 20 years event), 26.4% of farmers in eastern Germany suffered simultaneous yield losses of at least 20% in winter wheat and winter barley, while 19.1% of farmers in eastern Germany suffered simultaneous yield losses of at least 20% in winter wheat and sugar beet. Farmers should therefore be encouraged to grow crops with more diverse phenological requirements throughout the year. [ABSTRACT FROM AUTHOR]

In the face of changing investment intentions, the integration of environmental, social and governance (ESG) considerations into portfolio optimization is becoming the norm. Indeed, the purely financial dimension of investments is beginning to give way to the sustainable or responsible dimension which aims to generate long-term financial returns. Such an investment strategy has the constraint of investing only in companies which, according to the rating agencies, best meet these three criteria. To study the impact of similar investment strategies on portfolio performance, we compared the performance of 3 portfolios constructed with different ESG preferences. Built on the basis of the Best-in-class approach, the first is composed of the highest rated assets (AAA and AA) while the second has average ratings (A and BBB) and the third of the worst ESG ratings (BB, B and CCC). The results obtained in a robust mean-LPM theoretical framework, we managed to show that a preference for stocks with average ESG ratings in the composition of a portfolio to have the best risk-return trade-off. [ABSTRACT FROM AUTHOR]

Intense human activities have increasingly reshaped the global nutrient cycle, causing frequent environmental issues owing to excessive nitrogen (N) and phosphorus (P) inputs. Therefore, it is necessary to explore the component structure, driving factors, and environmental impacts of regional nutrient inputs. Based on net anthropogenic N and P input (NANI and NAPI, respectively) models, combined with data mining and statistical analysis, the spatiotemporal changes of NANI and NAPI in the Yangtze River Basin were studied. Their environmental and scale effects, policy impacts, and classification management were then discussed. The results reveal that NANI and NAPI showed a significant downward trend in the Yangtze River Basin from 2011 to 2019, with an average value of 7968 kg N km−2 year−1 and 1241 kg P km−2 year−1, respectively. Moreover, the contribution of varying fertilizer intensity resulted in an approximate change in both NANI and NAPI by 50%. Meanwhile, NANI and NAPI exhibited decreasing spatial trends from east to west and north to south, with developed agricultural plain areas and densely populated urban agglomeration areas being the focal areas of nutrient inputs. Despite the spatiotemporal differences, there was a strong dependence between higher nutrient input and higher nutrient concentration conditions. To relieve the environmental pressure, the fertilizer policy was implemented and had a marked impact on the change in nutrient input trend. Based on the classification of cities through the comparison of major input items, plain regions where fertilizer dominates nutrient input need to be managed by improving the utilization rate of fertilizer. [ABSTRACT FROM AUTHOR]

To improve the dynamic assessment of risks of speculative assets, we apply a Markov switching MGARCH approach to portfolio risk forecasting. More specifically, we take advantage of the flexible Markov switching copula multivariate GARCH (MS‐C‐MGARCH) model of Fülle and Herwartz (2022). As an empirical illustration, we take the perspective of a risk‐averse agent and employ the suggested model for assessments of future risks of portfolios composed of a high‐yield equity index (S&P 500) and two safe‐haven investment instruments (i.e., Gold and US Treasury Bond Futures). We follow recent suggestions to employ the expected shortfall as a prime assessment of tail risks. To accurately evaluate the merits of the new model, we back‐test the risk forecasting for daily returns over 10 years for heterogeneous market environments including, for example, the COVID‐19 pandemic. We find that the MS‐C‐MGARCH model outperforms benchmark volatility models (MGARCH, C‐MGARCH) in predicting both value‐at‐risk and expected shortfall. The superiority of the MS‐C‐MGARCH model becomes stronger, when the share of comparably risky assets in the portfolio is relatively large. [ABSTRACT FROM AUTHOR]

In this study, we propose the application of the GARCH‐EVT‐Copula model in estimating liquidity‐adjusted value‐at‐risk (L‐VaR) of energy stocks while modeling nonlinear dependence between return and bid‐ask spread. Using the L‐VaR framework of Bangia et al. (1998), we present a more parsimonious model that effectively captures non‐zero skewness, excess kurtosis, and volatility clustering of both return and spread distributions of energy stocks. Moreover, to measure the nonlinear dependence between return and spread series, we use multiple copulas: Clayton, Gumbel, Frank, Normal, and Student‐t. Based on the statistical backtesting and economic loss functions, our results suggest that the GARCH‐EVT‐Clayton copula is superior and most consistent in forecasting L‐VaR compared with other competing models. This finding has several implications for investors, market makers, and daily traders who appreciate the importance of liquidity in market risk computation. [ABSTRACT FROM AUTHOR]

The increase in world temperature or global warming is a form of imbalance in the average temperature on Earth. The increase in air temperature will increase the risk of disasters, which will occur more frequently in the future. Rising global temperatures are expected to cause changes that can have fatal consequences. To anticipate the dangers are predicted by predicting the future air temperature increase. One of the methods that can be used is spatial extreme value theory, which uses the Gaussian copula model approach and Student's t copula, where the choice of these two methods was based on the flexibility they offer in capturing tail dependencies due to their capacity to describe the dependence structure between many variables simultaneously. . This makes it possible to get a return level or predicted value of air temperature by considering the elements of location in it. This research discusses both approaches and uses the maximum likelihood estimation (MLE) and pseudo maximum likelihood estimation (PMLE) methods to estimate the parameters. In addition, since spatial elements need to be considered, the trend surface model is also used. Akaike information criterion (AIC) is used to determine the best model for predicting air temperature based on extreme n air temperature data in East Java Province from nine air temperature observation stations. The results show that the highest air temperature value is around the Banyuwangi temperature observation station located in Banyuwangi Regency in the next two-year return period. The AIC results show that the best model produced is the Gaussian copula approach with a smaller AIC value than the student's t-copula approach, which is 8.0174. This value used to compare the relative quality of different statistical models with a lower AIC value generally indicates a better-fitting model.This value with a lower AIC value generally indicates a better-fitting model.

The goal of this research was to examine tail dependence structures between selected commodity futures returns. Tail dependence, called also extremal dependence, was evaluated for the pairs of commodities coming from the same sector (energy or agricultural). The study covers the years 2018-2023, embracing the COVID-19 pandemic and the outbreak of the Russia-Ukraine war. To achieve the goal, bivariate dynamic models were applied to percentage log returns of commodity futures. Marginal distributions were described using the ARMA-GARCH models. Joint distributions were constructed using the symmetrized Joe-Clayton copula, which allowed to model asymmetric dependence in the tails of a distribution. Time variation of the copula parameters, here equal to tail dependence coefficients, was described using the evolution equations [Patton 2006]. In the energy sector, the dependence in both tails of analyzed distributions was relatively strong, dynamic and higher in the lower tail than in the upper tail. On the contrary, the agricultural sector lacks common patterns of tail dependency. This feature of the agricultural sector creates an opportunity for investors or risk managers to build well-diversified portfolios.

Teleconnection patterns are one of the causes of precipitation fluctuations in various regions of the world, including Iran. This study aims to develop bivariate models for forecasting autumn precipitation in the north-western region of Iran based on teleconnection indices. Copula functions were selected for this assignment due to the nonlinear relationship between precipitation and the teleconnection indices, as well as the fact that the assumption of normal distribution for precipitation data is not met, rendering Pearson correlation inappropriate. The dependence of Pacific and Atlantic Ocean teleconnection indices with precipitation for the period 1991-2020 was calculated using Kendall's and Pearson's rank correlation coefficients for moving average of one to six months. Appropriate copulas and marginal distributions were then used to model precipitation, and the performance of the developed models was evaluated. The results showed that the strongest correlations were obtained between the precipitation and the NINO3.4, SOI, and MEI indices. Consequently, the bivariate models using these indices demonstrated higher efficiency in simulating precipitation anomalies. Among these models, the one with the NINO3.4 predictor provided the best estimate of precipitation anomaly for 2021 and 2022, with values of -4.2 mm and -5.8 mm, respectively.

In reliability engineering, it is frequently encountered that multiple performance characteristics (PCs) deteriorate simultaneously. The associated degradation processes are usually dependent and exhibit some heterogeneity from unit to unit, which makes the multivariate degradation modeling and reliability evaluation more challenging. To this end, we propose a new multivariate gamma process model. This model introduces a multivariate random vector, whose joint distribution is constructed by marginal gamma distributions and a copula function, to describe the unit‐to‐unit variability and the dependence among PCs. Meanwhile, it does not require all PCs to be inspected at the same time points in contrast to the traditional copula‐based degradation models. In addition, two reliability evaluation methods are developed. Model parameters are estimated by the stochastic expectation maximization algorithm, and a three‐step procedure is provided to initialize this algorithm. Subsequently, numerical simulations are implemented to verify the proposed methods. Finally, two examples are provided for illustration, and it is shown that the proposed model and methods scale well to the degradation data with different numbers of PCs. What is more, comparisons with several benchmark models are performed, and the superiority of the proposed model is well demonstrated. [ABSTRACT FROM AUTHOR]

Incorporating realistic sets of patient-associated covariates, i.e., virtual populations, in pharmacometric simulation workflows is essential to obtain realistic model predictions. Current covariate simulation strategies often omit or simplify dependency structures between covariates. Copula models are multivariate distribution functions suitable to capture dependency structures between covariates with improved performance compared to standard approaches. We aimed to develop and evaluate a copula model for generation of adult virtual populations for 12 patient-associated covariates commonly used in pharmacometric simulations, using the publicly available NHANES database, including sex, race-ethnicity, body weight, albumin, and several biochemical variables related to organ function. A multivariate (vine) copula was constructed from bivariate relationships in a stepwise fashion. Covariate distributions were well captured for the overall and subgroup populations. Based on the developed copula model, a web application was developed. The developed copula model and associated web application can be used to generate realistic adult virtual populations, ultimately to support model-based clinical trial design or dose optimization strategies. [ABSTRACT FROM AUTHOR]

The motivation of this work came when we were trying to analyze gold price data of the Indian market and the exchange rate data between Indian Rupees and US Dollars. It is observed that in both the cases there is a significant amount of time when X n = X n + 1 , hence they cannot be ignored. In this paper we have introduced a very flexible discrete time and continuous state space stationary stochastic process { X n } , where X n has a proportional hazard class of distribution and there is a positive probability that X n = X n + 1 . We have assumed a very flexible piecewise constant hazard function of the base line distribution of the proportional hazard class. Various properties of the proposed class has been obtained. Various dependency properties have been established. Estimating the cut points of the piecewise constant hazard function is an important problem and it has been addressed here. The maximum likelihood estimators (MLEs) of the unknown parameters cannot be obtained in closed form, and we have proposed to use profile likelihood method to compute the estimators. The gold price data set and the exchange rate data set have been analyzed and the results are quite satisfactory. [ABSTRACT FROM AUTHOR]

Objectives. The objective of the study is to use copula models to analyze shares of the Russian stock market and describe changes in the relationship between the shares before and during the coronavirus infection (COVID-19).Methods. An algorithm for using copulas and functions of the R programming language in its implementation is presented. To model the dynamics of financial series the ARMA-GJR-GARCH process (autoregressive moving average Glosten-Jagannathan-Runkle model with generalized autoregressive conditional heteroskedasticity) is used. The selection of optimal families and parameters of copula models is carried out. The adequacy of the obtained models is checked and the results of the study of the relationship between the series are analyzed.Results. An algorithm has been developed for a relatively new approach to using copulas in conjunction with the ARMA-GJR-GARCH model. The approach was used to study the impact of coronavirus in the context of the Russian economy. It is revealed that during the COVID-19 period the dependence between different stocks increases. It is shown that the effect of volatility in financial series increases after the outbreak of the pandemic.Conclusion. The research algorithm using copula models in conjunction with the ARMA-GJR-GARCH process has shown its feasibility. This approach can be used with other GARCH-type models to study finance and other areas.

Flood frequency in river source regions is significantly affected by rainfall and snowmelt as part of climatic changes. A traditional univariate flood frequency analysis cannot reflect the complexity of floods, and when used in isolation, it can only underestimate flood risk. For effective flood prevention and mitigation, it is essential to consider the combined effects of precipitation and snowmelt. Copula functions can effectively quantify the joint distribution relationship between floods and their associated variables without restrictions on their distribution characteristics. This study uses copula functions to consider a multivariate probability distribution model of flood peak flow (Q) with cumulative snowmelt (CSm) and cumulative precipitation (CPr) for the Hutubi River basin located in northern Xinjiang, China. The joint frequencies of rainfall and snowmelt floods are predicted using copula models based on the Coupled Model Intercomparison Project Phase 6 data. The results show that Q has a significant positive correlation with 24-d CSm (r = 0.559, p = 0.002) and 23-d CPr (r = 0.965, p

This paper proposes an efficient method for quantifying the stratigraphic uncertainties and modeling the geological formations based on boreholes. Two Markov chains are used to describe the soil transitions along different directions, and the transition probability matrices (TPMs) of the Markov chains are analytically expressed by copulas. This copula expression is efficient since it can represent a large TPM by a few unknown parameters. Due to the analytical expression of the TPMs, the likelihood function of the Markov chain model is given in an explicit form. The estimation of the TPMs is then re-casted as a multi-objective constrained optimization problem that aims to maximize the likelihoods of two independent Markov chains subject to a set of parameter constraints. Unlike the method which determines the TPMs by counting the number of transitions between soil types, the proposed method is more statistically sound. Moreover, a random path sampling method is presented to avoid the directional effect problem in simulations. The soil type at a location is inferred from its nearest known neighbors along the cardinal directions. A general form of the conditional probability, based on Pickard's theorem and Bayes rule, is presented for the soil type generation. The proposed stratigraphic characterization and simulation method is applied to real borehole data collected from a construction site in Wuhan, China. It is illustrated that the proposed method is accurate in prediction and does not show an inclination during simulation.

AbstractIn the context of actuarial science, the second largest claim amount is crucial to insurance analysis since they provide useful information for determining annual premium. In this article, we provide sufficient conditions of the second largest claim amounts arising from two sets of dependent and heterogeneous individual risk models according to various stochastic orders. It is first shown that the reversed hazard order between the occurrence probabilities vectors implies the reversed hazard order of the second largest claim amounts under certain conditions. Second, sufficient conditions are established for the usual stochastic ordering of the second largest claim amounts arising from heterogeneous dependent individual risk models under copula dependence. Finally, several examples illustrating the theoretical results are presented as well. [ABSTRACT FROM AUTHOR]

Structural planes are one of the key factors controlling the stability of rock masses. A comprehensive understanding of the spatial distribution characteristics of structural planes is essential for accurately identifying key blocks, analyzing rock mass stability, and addressing various rock engineering challenges. This study compares the effectiveness of four stochastic structural plane generation methods—the Monte Carlo method, the Copula-based method, generative adversarial networks (GAN), and denoised diffusion models (DDPM)—in generating stochastic structural planes and capturing potential correlations between structural plane parameters. The Monte Carlo method employs the mean and variance of three parameters of the measured factual structural planes to generate data that follow the same distributions. The other three methods take the entire set of measured factual structural planes as the overall input to generate structural planes that exhibit the same probability distributions. Five sets of structural planes on four rock slopes in Norway are examined as an example. The validation and analysis were performed using histogram comparison, data feature comparison, scatter plot comparison, and linear regression analysis. The results show that the Monte Carlo method fails to capture the potential correlation between the dip direction and dip angle despite the best fit to the measured factual structural planes. The Copula-based method performs better with smaller datasets, and GAN and DDPM are better at capturing the correlation of measured factual structural planes in the case of large datasets. Therefore, in the case of a limited number of measured structural planes, it is advisable to employ the Copula-based method. In scenarios where the dataset is extensive, the deep generative model is recommended due to its ability to capture complex data structures. The results of this study can be utilized as a valuable point of reference for the accurate generation of stochastic structural planes within rock masses. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper proposes several novel classes of independence tests specially designed for count data. The tests are based on the difference between joint and marginal probability generating functions and can be applied to count data of any arbitrary fixed dimension. The limiting properties of the test statistics are explored. The competitiveness of the novel proposal is demonstrated through an extensive empirical study, while the application is illustrated with a few real-data examples. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data frequently occur in many areas and a great deal of literature on their analyses has been established. In this article, we discuss the situation where one faces bivariate interval-censored data arising from case-cohort studies, which are commonly used as a tool to save costs when disease incidence is low and covariates are difficult to obtain. For this problem, a class of copula-based semi-parametric models is presented and for estimation, a sieve weighted maximum likelihood estimation procedure is developed. The resulting estimators of regression parameters are shown to be strongly consistent and asymptotically normal. Furthermore, the proposed method is generalized to the situation of non rare diseases. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it performs well in practice. [ABSTRACT FROM AUTHOR]

Generally, insurance companies face challenges in determining the Capital Requirement (CR) which is essential for business continuity. This situation could worsen if substantial number and amount of claims are requested by policyholders due to losses from catastrophic events such as floods, tsunamis, and earthquakes. In this paper, we propose a structured model to determine the CR for non-life insurance companies through loss ratios. Firstly, dependence structure among the business lines is modelled using copulas from both Elliptical and Archimedean copulas family with loss ratios from four business lines as the risk factors. The loss ratios are derived from incurred claims and earned premiums data of Malaysia’s non-life insurance businesses, such as Fire insurance, Motor insurance, Marine, Aviation and Transport (MAT) insurance, and Miscellaneous insurance. Subsequently, a combination of popular risk measures such as Value-at-Risk (VaR) and TailValue-at-Risk (TVaR) with a Drawable Vine (D-Vine) copulas model known as hybrid model is developed to estimate insurance companies’ risk capital. Finally, a simulation of Monte Carlo is commanded by calibrating data with our selected model to project the CR. This study contributes to the literature by addressing the problem of determining the appropriate CR for non-life insurance companies, proposing an empirical model based on real non-life insurance company data with a hybrid model built from risk measures and D-Vine copula. [ABSTRACT FROM AUTHOR]

We propose a method to obtain a new class of copulas using a probability generating function (PGF) of positive-integer valued random variable. Some existing copulas in the literature are sub-families of the proposed copulas. Various dependence measures and invariant property of the tail dependence coefficient under PGF transformation are also discussed. We propose an algorithm for generating random numbers from the PGF copula. The bivariate concavity properties, such as Schur concavity and quasi-concavity, associated with the PGF copula are studied. Two new generalized FGM copulas are introduced using PGFs of geometric and discrete Mittag-Leffler distributions. The proposed two copulas improved the Spearman's rho of FGM copula by (−0.3333, 0.4751) and (−0.3333, 0.9573). Finally, we analyse a real dataset to illustrate the practical application of the proposed copulas. [ABSTRACT FROM AUTHOR]

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL. [ABSTRACT FROM AUTHOR]

Some of the collected data by wireless sensor networks (WSNs) often digress from the normal pattern of the set and are called the 'outliers' or 'anomalies'. These outlier data are usually derived from an error that can be due to the constraints of sensor nodes such as problems in the processing unit, power supply, and component failure or an event occurring at the development site of sensor nodes, including the earthquake or flood, affecting the quality of the collected data and their reliability for decision making. In this work, a method is proposed for detecting outlier data in networks based on the hidden Markov model and the copula theory. Copula was used because of its ability to deal with multivariate sets and its unlimitedness in such a way that it required no assumption about data distribution, and Markov has been applied due to its good performance in forecasting. The results of evaluations on the actual data from the Intel laboratory represent the efficiency of the proposed method. Bases on the performance evaluations of the proposed method, in comparison with a relatively new work leading to good results. [ABSTRACT FROM AUTHOR]

An emerging area of study known as Cognitive IoT (CIoT) has emerged as a result of recent efforts to include cognition in the design of the Internet of Things (IoT). Several features and challenges from the IoT are carried over to the CIoT. A lot of applications in CIoT generate massive heterogeneous data, and they require inferential tasks with less computational overhead. Therefore, this study suggests a decentralized computing approach to handle multiple hypothesis testing in less computational time. The first stage is to minimize error at the cluster node by total variance regularization through the alternating direction method of multipliers. Subsequently, the fusion center handles the heterogeneity of data, minimizes model error, extracts the most informative data, and adjusts the p-value for multiple hypotheses testing. The experimental evaluation and cross-validation on six-month traces of the carbon monoxide dataset reveal the efficacy of the proposed algorithm over competing approaches. [ABSTRACT FROM AUTHOR]

This study seeks to investigate the extreme risk spillovers from crude oil to four major Asian stock markets from a market sentiment perspective. A copula-CoVaR (Conditional Value-at-Risk) approach is adopted to construct a dynamic network to capture the contributions of different types of market sentiment to the evolution of oil-stock risk nexus. The empirical evidence shows the presence of significant risk spillover effects from crude oil to equity markets. The dynamics of the oil-to-stock risk spillovers is shown to be significantly driven by market sentiments, mainly market fears in both stock markets and crude oil market triggered by prominent systemic events. As an extreme event unfolds, the oil-to-stock risk spillover dynamics is increasing susceptible to escalating market fears. [ABSTRACT FROM AUTHOR]