Search Results (21)

COVID-19’s effects on mortality are hard to quantify. Issues with attribution can cause problems with resulting conclusions. Analyzing excess mortality addresses this concern and allows for the analysis of broader effects of the pandemic. We propose separate ARIMA models to analyze excess mortality for several countries. For the model of joint excess mortality, we suggest vine copulas with Bayesian pair copula selection. This is a new methodology and after its discussion we offer an illustration. The present study examines weekly mortality data from 2019 to 2022 in the USA, Canada, France, Germany, Norway, and Sweden. Previously proposed ARIMA models have low lags and no residual autocorrelation. Only Norway’s residuals exhibited normality, while the remaining residuals suggest skewed Student t-distributions as a plausible fit. A vine copula model was then developed to model the association between the ARIMA residuals for different countries, with the countries farther apart geographically exhibiting weak or no association. The validity of fitted distributions and resulting vine copula was checked using 2023 data. Goodness of fit tests suggest that the fitted distributions were suitable, except for the USA, and that the vine copula used was also valid. We conclude that the time series models of COVID-19 excess mortality are viable. Overall, the suggested methodology seems suitable for creating joint forecasts of pandemic mortality for several countries or geographical regions. Full article

Weather derivative markets, particularly Chicago Mercantile Exchange (CME) Heating Degree Day (HDD) and Cooling Degree Day (CDD) futures, face challenges from complex temperature dynamics and spatially heterogeneous co-extremes that standard Gaussian models overlook. Using daily data from 13 major U.S. cities (2014–2024), we first construct a two-stage baseline model to extract standardized residuals isolating stochastic temperature deviations. We then estimate the Extreme Value Index (EVI) of HDD/CDD residuals, finding that the nonlinear degree-day transformation amplifies univariate tail risk, notably for warm-winter HDD events in northern cities. To assess multivariate extremes, we compute Tail Dependence Coefficient (TDC), revealing pronounced, geographically clustered tail dependence among HDD residuals and weaker dependence for CDD. Finally, we compare Gaussian, Student’s t, and Regular Vine Copula (R-Vine) copulas via joint VaR–ES backtesting. The R-Vine copula reproduces HDD portfolio tail risk, whereas elliptical copulas misestimate portfolio losses. These findings highlight the necessity of flexible dependence models, particularly R-Vine, to set margins, allocate capital, and hedge effectively in weather derivative markets. Full article

The Student’s t-distribution provides a thematic connection between the historical and technical elements of this paper. The historical section offers a brief account of the early contributions of Chris Heyde and his collaborations with Madan and Seneta in the development of financial mathematics. The technical section focuses on hypothesis testing, motivated by the observation that, in a setting with pairwise exchangeable dependence for test statistics, the cutoff methods proposed by Sarkar and colleagues in 2016 can be viewed as a first iteration of the classical approach developed by Holm in 1979. These methods had already been refined earlier by Seneta and Chen in their work from 1997 and 2005, which laid the foundation for further improvements. Building on this, a new iteration of the Seneta-Chen method is presented, offering enhancements over the Sarkar approach. Numerical and graphical comparisons are provided, focusing on equal tails testing within the multivariate t-distribution framework. While the tabulated results clearly show improvements with the new procedure, the simulated family-wise error rates across varying correlations reveal only minor practical differences between the iterative methods. This suggests that, under suitable conditions, a single iteration suffices in practice. The paper concludes with personal reflections from the first author, sharing memories of Joe Gani and Chris Heyde, in keeping with the commemorative nature of this issue. Full article

As an extension of the (univariate) Birnbaum–Saunders distribution, the Type-II generalized crack (GCR2) distribution, built on an appropriate base density, provides a sufficient level of flexibility to fit various distributional shapes, including heavy-tailed ones. In this paper, we develop a bivariate extension of the Type-II generalized crack distribution and study its dependency structure. For practical applications, three specific distributions, GCR2-Generalized Gaussian, GCR2-Student’s t, and GCR2-Logistic, are considered for marginals. The expectation-maximization algorithm is implemented to estimate the parameters in the bivariate GCR2 models. The model fitting results on a catastrophic loss dataset show that the bivariate GCR2 distribution based on the generalized Gaussian density fits the data significantly better than other alternative models, such as the bivariate lognormal distribution and some Archimedean copula models with lognormal or Pareto marginals. Full article

Financial markets are increasingly interlinked. Therefore, this study explores the complex relationships between the Tadawul All Share Index (TASI), West Texas Intermediate (WTI) crude oil prices, and Bitcoin (BTC) returns, which are pivotal to informed investment and risk-management decisions. Using copula-based models, this study identified Student’s t copula as the most appropriate one for encapsulating the dependencies between TASI and BTC and between TASI and WTI prices, highlighting significant tail dependencies. For the BTC–WTI relationship, the Frank copula was found to have the best fit, indicating nonlinear correlation without tail dependence. The predictive power of the identified copulas were compared to that of Long Short-Term Memory (LSTM) networks. The LSTM models demonstrated markedly lower Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Scaled Error (MASE) across all assets, indicating higher predictive accuracy. The empirical findings of this research provide valuable insights for financial market participants and contribute to the literature on asset relationship modeling. By revealing the most effective copulas for different asset pairs and establishing the robust forecasting capabilities of LSTM networks, this paper sets the stage for future investigations of the predictive modeling of financial time-series data. The study highlights the potential of integrating machine-learning techniques with traditional econometric models to improve investment strategies and risk-management practices. Full article

In this study, we assess COVID-19-related mortality in Minnesota and Wisconsin with the aim of demonstrating both the temporal dynamics and the magnitude of the pandemic’s influence from an actuarial risk standpoint. In the initial segment of this paper, we discuss the methodology successfully applied to describe associations in financial and engineering time series. By applying time series analysis, specifically the autoregressive integrated with moving average methods (ARIMA), to weekly mortality figures at the national or state level, we subsequently delve into a marginal distribution examination of ARIMA residuals, addressing any deviation from the standard normality assumption. Thereafter, copulas are utilized to architect joint distribution models across varied geographical domains. The objective of this research is to offer a robust statistical model that utilizes observed mortality datasets from neighboring states and nations to facilitate precise short-term mortality projections. In the subsequent section, our focus shifts to a detailed scrutiny of the statistical interdependencies manifesting between Minnesota and Wisconsin’s weekly COVID-19 mortality figures, adjusted for the time series structure. Leveraging open-source data made available by the CDC and pertinent U.S. state government entities, we apply the ARIMA methodology with subsequent residual distribution modeling. To establish dependence patterns between the states, pair copulas are employed to articulate the relationships between the ARIMA residuals, drawing from fully parametric models. We explore several classes of copulas, comprising both elliptic and Archimedean families. Emphasis is placed on copula model selection. Student t-copula with the marginals modeled by non-standard t-distribution is suggested for ARIMA residuals of Minnesota and Wisconsin COVID mortality as the model of choice based on information criteria and tail cumulation. The copula approach is suggested for the construction of short-term prediction intervals for COVID-19 mortality based on publicly available data. Full article

Evidence that cryptocurrencies exhibit speculative bubble behavior is well documented. This evidence could trigger global financial instability leading to systemic risk. It is therefore crucial to quantify systemic risk and investigate its transmission mechanism across crypto markets and other global financial markets. We can accomplish this using the so-called multivariate conditional value-at-risk (MCoVaR), which measures the tail risk of a targeted asset from each market conditional on a set of multiple assets being jointly in distress and on a set of the remaining assets being jointly in their median states. In this paper, we aimed to find its analytic formulas by considering multivariate copulas, which allow for the separation of margins and dependence structures in modeling the returns of the aforementioned assets. Compared to multivariate normal and Student’s t benchmark models and a multivariate Johnson’s SU model, the copula-based models with non-normal margins produced a MCoVaR forecast with superior conditional coverage and backtesting performances. Using a corresponding Delta MCoVaR, we found the crypto assets to be potential sources of systemic risk jointly transmitted within the crypto markets and towards the S&P 500, oil, and gold, which was more apparent during the COVID-19 period encompassing the recent 2021 crypto bubble event. Full article

The cryptocurrency market offers significant investment opportunities but also entails higher risks as compared to other asset classes. This article aims to analyse the financial risk characteristics of individual cryptocurrencies and of a broad cryptocurrency market portfolio. We construct a portfolio comprising the 20 largest cryptocurrencies, which cover 82.1% of the total cryptocurrency market. The returns are examined for extreme tail risks by the application of Extreme Value Theory. We utilise the GARCH-EVT approach in combination with a novel algorithm to automatically determine the optimal threshold to model the tail distribution. Furthermore, we aggregate the individual market risks with a t-Student Copula to investigate possible diversification effects on a portfolio level. The empirical analysis indicates that all examined cryptocurrencies show high volatility in their price movements, whereby Bitcoin acts as the most stable cryptocurrency. All return distributions are heavy-tailed and subject to extreme tail risks. We find strong, positive intra-market correlations, in particular with the two largest cryptocurrencies Bitcoin and Ethereum. No diversification effect can be achieved by aggregating market risks. On the contrary, a negligibly lower expected return and higher joint extreme returns can be observed. From this analysis, it can be concluded that investments in individual cryptocurrencies as well as in a portfolio show extreme risks of losses. From the investor’s point of view, a possible strategy of risk reduction through portfolio formation within cryptocurrencies is only promising to a limited extent and does not offer a satisfactory solution to significantly reduce the risk within this asset class. Full article

This paper attempted to apply an EVT-based pairwise copula method for modelling risk interaction between foreign exchange rates and equity indices of the Johannesburg Stock Exchange (JSE) and to model the dependence structure of the underlying assets with some selected listed stock indices. We filtered the return residuals using the stochastic volatility and GJR-GARCH (1,1) models with different distributions, and we selected the best-fitted model in the GARCH framework. We applied the peaks-over-threshold (POT) method to the filtered residuals to fit it by the generalised Pareto distribution (GPD), and we used the vine copula to model the co-movement between foreign exchange rates and equity indices and value at risk (VaR) for risk quantification. We used three exchange rates (USD, GDP, and EUR) against the South African rand (ZAR) and six industry indices (banking, life insurance, non-life insurance, leisure, telecommunications, and mining). Our empirical findings show that the GJR-GARCH with Student’s t-distribution, combined with a regular (R)-vine copula, outperforms the alternatives models. Dependence structure analysis reveals a strong co-dependency between the stock from the financial industry and foreign exchange rates. The results also show that VaR-based R-vine copula outperforms the model compared to VaR-based D-vine and C-vine before the COVID-19 outbreak, while the D-vine copula produced appears to be the most suitable risk model specification for quantifying risk during the COVID-19 pandemic. Therefore, VaR-based R-vine copula is suitable for risk quantification, while GJR-GARCH with Student’s t-distribution produces better results in the GARCH framework. Further, we find that equity indices and foreign exchange rates exhibit higher tail risk contagion during the COVID-19 pandemic, with the non-life-insurance and telecommunications sectors appearing to be the investor’s safe haven among the listed sectors of the JSE. Our results will help South African investors seek risk-adjusted returns to substantially reduce the hedging cost of potential loss due to the misspecification of a risk model and make an investment decision during the global health crisis. Full article

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples. Full article

Bivariate modeling and hazard assessment of low flows are performed exploiting copulas. 7-day low flows observed, respectively, in the upper, middle and lower parts of the Çoruh basin (Turkey) are examined, considering three pairs of certified stations located in different sub-basins. A thorough statistical analysis indicates that the GEV distribution can be used to model the marginal behavior of the low-flow. The joint distributions at each part are modeled via a dozen of copula families. As a result, the Husler–Reiss copula adequately fits the joint low flows in the upper part, while the t-Student copula turns out to best fit the other parts. In order to assess the low-flow hazard, these copulas are then used to compute joint return periods and failure probabilities under a critical bivariate “AND” hazard scenario. The results indicate that the middle and lower parts of the Çoruh basin are likely to experience the largest drought hazards. As a novelty, the statistical tools used allow to objectively quantify drought threatening in a thorough multivariate perspective, which involves distributional analysis, frequency analysis (return periods) and hazard analysis (failure probabilities). Full article

Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems’ output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR). Full article

This paper analyzes the volatility dynamics in the financial markets of the (three) most powerful countries from a military perspective, namely, the U.S., Russia, and China, during the period 2015–2018 that corresponds to their intervention in the Syrian war. As far as we know, there is no literature studying this topic during such an important distress period, which has had very serious economic, social, and humanitarian consequences. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH (1, 1)) model yielded the best volatility results for the in-sample period. The weighted historical simulation produced an accurate value at risk (VaR) for a period of one month at the three considered confidence levels. For the out-of-sample period, the Monte Carlo simulation method, based on student t-copula and peaks-over-threshold (POT) extreme value theory (EVT) under the Gaussian kernel and the generalized Pareto (GP) distribution, overstated the risk for the three countries. The comparison of the POT-EVT VaR of the three countries to a portfolio of stock indices pertaining to non-military countries, namely Finland, Sweden, and Ecuador, for the same out-of-sample period, revealed that the intervention in the Syrian war may be one of the pertinent reasons that significantly affected the volatility of the stock markets of the three most powerful military countries. This paper is of great interest for policy makers, central bank leaders, participants involved in these markets, and all practitioners given the economic and financial consequences derived from such dynamics. Full article

Natural disasters such as dust storms are random phenomena created by complicated mechanisms involving many parameters. In this study, we used copula theory for bivariate modeling of dust storms. Copula theory is a suitable method for multivariate modeling of natural disasters. We identified 40 severe dust storms, as defined by the World Meteorological Organization, during 1982–2017 in Yazd province, central Iran. We used parameters at two spatial vertical levels (near-surface and upper atmosphere) that included surface maximum wind speed, and geopotential height and vertical velocity at 500, 850, and 1000 hPa. We compared two bivariate models based on the pairs of maximum wind speed–geopotential height and maximum wind speed–vertical velocity. We determined the bivariate return period using Student t and Gaussian copulas, which were considered as the most suitable functions for these variables. The results obtained for maximum wind speed–geopotential height indicated that the maximum return period was consistent with the observed frequency of severe dust storms. The bivariate modeling of dust storms based on maximum wind speed and geopotential height better described the conditions of severe dust storms than modeling based on maximum wind speed and vertical velocity. The finding of this study can be useful to improve risk management and mitigate the impacts of severe dust storms. Full article

The purpose of this paper is to analyze the impact of trade openness and the factors based on the gravity model on the bilateral trade flows between Thailand and Japan. The factors consist of GDP, distance, trade openness, and exchange rate. Bilateral trade is composed of two flows: Thailand’s export flow to Japan, and Thailand’s import flow from Japan. The specified gravity equations are estimated by Copula-based Markov switching seemingly unrelated regression approach. The best-fitting model is chosen based on the lowest Akaike information criterion (AIC) and Bayesian information criterion (BIC). The Normal and Student’s t distributions are for Thailand’s export equation and Thailand’s import equation, respectively. The Student’s t copula is applied for joint distribution. Analyzing the bilateral trade flow is separated into two situations, namely the high and the low growth markets. Empirical results show that distance provides a positive effect on the export in a high growth regime, but a negative impact on the export in a low growth regime. As for Thailand’s import flow, all variables, but especially trade openness, provide strong evidence supporting significance for both regimes. For the GDPs of both Thailand and Japan, trade openness and the exchange rate increase import flow in a high growth market. Meanwhile, the exchange rate decreases import flow in a low growth market. The Markov Switching Probability Estimation notes that Thailand’s trading with Japan is mostly in the fast-growing market. Full article