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Balochistan province is highly drought-prone and affected by almost every drought in Pakistan. This study is conducted to evaluate and project drought for the planning of water resources in Baluchistan, Pakistan. Drought characteristics of duration and severity were extracted from the standardized precipitation index (SPI). Statistical tools showed a high positive correlation and skewed nature between drought duration and severity. The sites were checked for identical drought conditions through homogeneity measures. Best-fitted regional probability distributions were selected for both drought characteristics and transformed into uniformly distributed values over [0, 1]. The bivariate Gumbel-Hougaard (G-H) copula function was selected for joint and conditional drought projections. The G-H copula function has the property to measure upper tail dependence which is highly important for measuring extreme drought conditions. Three types of joint and two types of conditional drought projections were found numerically and graphically using selected years of return periods. Contour lines were drawn for possible combinations of drought duration and severity to show the drought variability within the region. According to projections, the drought duration and severity increase with the increase in return periods. Conditional projections have high values of severity (or duration) return periods because drought at a fixed duration (or severity) takes a long time to occur. The results show changes in drought conditions and might help in drought mitigation and water planning in Balochistan, Pakistan. There is no such detailed study of drought risk assessment in the area. This effort will fill the research gap in the existing literature in the study area. [ABSTRACT FROM AUTHOR]

Hydrological process is very complex, so it is difficult for one copula to describe dependence patterns between two hydrological variables comprehensively (dependence pattern refers to the correlation and tail dependence between two random variables). This paper applied a linear weighted function of Gumbel copula, Clayton copula and Frank copula (coupled copula) to study dependence patterns between two hydrological variables and take precipitation as an example. Two experiments to study the joint probabilistic characteristics of the daily precipitation sequences in summer at two pairs of stations on the tributaries of Jinghe are performed to test our new method and compared with Gumbel copula, Clayton copula and Frank copula. Both experiments indicate that the coupled copula is superior to study the upper tail dependence, lower tail dependence and symmetric tail dependence between two precipitation sequences simultaneously. Moreover, the coupled copula is applied to estimate the joint return periods and conditional probabilities, and the joint return periods are 57.5 and 59.6 when the designed return period is 100. The result shows that there is a high probability of occurrence of precipitation extremes at the Huanxian and Xifeng stations when once in a 1000 or 100 years daily precipitation occur at the Guyuan and Pingliang stations. The coupled copula can also be applied in flood and drought frequency analysis. [ABSTRACT FROM AUTHOR]

We explore extreme return-volumes dependence among different cryptocurrencies such as Bitcoin, Ethereum, Ripple, and Litecoin by using the Copula approach. We use Student-t, Frank, Clayton, Survival Clayton, Gumbel, and SJC copulas. We filter out margins by using the EGARCH model for return series and GARCH model for volume series. Evidence of significant symmetric dependence between return-volume is not found due to insignificance of student-t and Frank copula parameters. In a return-volume relationship, coefficients of lower tail dependence are significant for Bitcoin, Ripple, and Litecoin which means that low returns are followed by low volumes. Lower tail dependence for the return-volume relationship is stronger than the upper tail dependence for Bitcoin, Ripple, and Litecoin. Moreover, for negative return-volume, left tail dependence coefficients are significant for Ripple and Litecoin, which means that high returns are followed by low volumes for Ripple and Litecoin. Our investigation shows that investors (buyer or seller) are very careful in extreme market conditions for both Ripple and Litecoin. Extreme upper tail and lower tail dependence coefficients are insignificant for Ethereum.

We explore extreme return-volumes dependence among different cryptocurrencies such as Bitcoin, Ethereum, Ripple, and Litecoin by using the Copula approach. We use Student-t, Frank, Clayton, Survival Clayton, Gumbel, and SJC copulas. We filter out margins by using the EGARCH model for return series and GARCH model for volume series. Evidence of significant symmetric dependence between return-volume is not found due to insignificance of student-t and Frank copula parameters. In a return-volume relationship, coefficients of lower tail dependence are significant for Bitcoin, Ripple, and Litecoin which means that low returns are followed by low volumes. Lower tail dependence for the return-volume relationship is stronger than the upper tail dependence for Bitcoin, Ripple, and Litecoin. Moreover, for negative return-volume, left tail dependence coefficients are significant for Ripple and Litecoin, which means that high returns are followed by low volumes for Ripple and Litecoin. Our investigation shows that investors (buyer or seller) are very careful in extreme market conditions for both Ripple and Litecoin. Extreme upper tail and lower tail dependence coefficients are insignificant for Ethereum. [ABSTRACT FROM AUTHOR]

Higlights • Finding a consistent and asymptotically unbiased estimator of integrated volatility for emerging markets under consideration. • Determining optimal slow frequency for two time scale estimation. • Employing the upper tail dependence (Gumbel copula) measure for comparison purposes, in addition to standard loss functions MSE and QLIKE. • Employing DM test in determining forecasting accuracy between competing OHLC estimators. • Recommending the appropriate ex-post daily volatility measure in the lack of high-frequency data for each emerging market under consideration. Abstract This paper explores the effectiveness of eight range-based volatility estimators for seven European emerging markets. It offers added value by: (i) finding a consistent and asymptotically unbiased estimator of integrated volatility for emerging markets, (ii) employing the upper tail dependence for comparison purposes, in addition to standard loss functions, and (iii) recommending the appropriate ex-post volatility measure in the lack of high-frequency data. When no strong preference for a specific estimator is found, the upper tail dependence measure is consulted, confirming the MSE-based ranking for Czech Republic, Greece, Poland, and Romania; and the QLIKE-based ranking for Bulgaria, Croatia, and Hungary. [ABSTRACT FROM AUTHOR]

This article extends the analysis of the Seemingly Unrelated Regression (SUR) Tobit model for two right-censored dependent variables by modeling its nonlinear dependence structure through the rotated by 180 degrees version of the Clayton copula. An advantage of our approach is to provide unbiased point estimates of the marginal and copula parameters. Moreover, we discuss the construction of confidence intervals using bootstrap resampling procedures. The results of the performed simulation study demonstrate the good performance of the proposed methods. We illustrate our procedures using bivariate customer churn data from a Brazilian commercial bank. [ABSTRACT FROM AUTHOR]

The simultaneous occurrence of extreme events, such as simultaneous storms and floods at different locations, has a serious impact on risk assessment and mitigation strategies. The joint occurrence of extreme events can be measured by the so-called upper tail dependence (UTD) coefficient λ. In this study, we reconsider the properties of the most popular λ estimators and show that their strong bias and uncertainty make most of the empirical results reported in the hydrological literature questionable. In order to overcome the limits of λ analysis, we test several alternative tools such as a pool of formal statistical tests devised for recognizing upper tail independence and graphical diagnostics based on binary correlation and binary entropy. The reliability of all the methods is preliminarily checked by Monte Carlo experiments. Statistical tests and graphical diagnostics are therefore applied to three different rainfall data sets that allow us to explore the properties of the spatial dependence structure of rainfall extremes over a wide range of spatio-temporal scales ranging from 30 min and 1 km to 30 days and $$\approx $$ 3000 km. Results highlight that (1) classical estimators provide non zero tail dependence even for cases where it should be zero; (2) formal tests and binary correlation highlight that the pairwise spatial dependence structure can be weaker than Gaussian, thus excluding UTD calculated in a pairwise manner; (3) the binary entropy computed on triples of locations shows that the pairwise UTD is not enough to explain the spatial dependence structure of extreme rainfall, whose complexity becomes evident only after resorting to higher order correlation measures. The results concerning the bias and uncertainty of λ estimators are fully general and suggest avoiding their use especially for the short time series usually available in hydrology. [ABSTRACT FROM AUTHOR]

This paper considers the tail behavior of Poisson shot noise processes where the shock random variables are generally dependent but bivariate upper tail independent. Some uniform asymptotic relations are established for tail probabilities of the process. As the Poisson shot noise process can capture the effects of delay factors and the interest factor in the insurance business, these established results are very useful in many insurance applications. As examples, they are applied to two important actuarial topics: ruin probabilities and insurance premium approximation. [ABSTRACT FROM AUTHOR]

In this paper we investigate the asymptotic behaviors of the finite- and infinite-time ruin probabilities fora Poisson risk model with stochastic investment returns which constitute a general adapted càdlàg process and heavy-tailed claim sizes which are bivariate upper tail independent. The results of this paper show lhat the asymptotic ruin probabilities are dominated by the extreme of insurance risk but not by that of investment risk. As applications of the results, we discuss four special cases when the investment returns are determined by a fractional Brownian motion, an integrated Vasicek model, an integrated Cox-Ingersoll-Ross model, and the Heston model. [ABSTRACT FROM AUTHOR]

This paper explores the joint extreme-value behavior of discontinuous random variables. It is shown that as in the continuous case, the latter ischaracterized by the weak limit of the normalized componentwise maxima and the convergence of any compatible copula. Illustrations are provided and an extension to the case of triangular arrays is considered which sheds new light on recent work of Coles and Pauli (Stat Probab Lett 54:373-379, 2001) and Mitov and Nadarajah (Extremes 8:357-370, 2005). This leads to considerations on the meaning of the bivariate upper tail dependence coefficient of Joe (Comput Stat Data Anal 16:279-297, 1993) in the discontinuous case. [ABSTRACT FROM AUTHOR]

Abstract: Consider the problem of approximating the tail probability of randomly weighted sums and their maxima, where is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class, and is a sequence of nonnegative random variables, independent of and satisfying certain moment conditions. Under the assumption that has no bivariate upper tail dependence along with some other mild conditions, this paper establishes the following asymptotic relations: and as . In doing so, no assumption is made on the dependence structure of the sequence . [Copyright &y& Elsevier]