Extreme Climatic Characteristics Near the Coastline of the Southeast Region of Brazil in the Last 40 Years

The southeastern Brazilian coast is a vulnerable region to the development of severe storms, mainly caused by the passage of cold fronts and extratropical cyclones. In the last decades, there has been an increase in the occurrence of subtropical cyclones. This study investigates trends and climatic variations, analyzing surface meteoceanographic series at six grid points from the reanalysis databases of ERA-Interim and ERA5 (European Center for Medium-Range Weather Forecasts-ECMWF) from 1979 to 2018 over the ocean region bounded, approximately, at 18°S, 25°S and 37ºW, 45ºW (between the states of Espírito Santo, Rio de Janeiro and São Paulo). Non-parametric statistical tests and the generalized extreme value distribution are employed for annual, seasonal and daily maxima/minima. The numbers of occurrence of extreme values, as well as the extremal index are also estimated in order to better understand the behavior of extremes. Annual maximum sea-surface temperature anomalies of the ERA-Interim databases show very low negative values, mainly at the beginning of measurements (between 1979 and 1982), leading to high positive trend values. The results are compared to the updated data from ERA5 which have anomalies that are more homogeneous with positive trends but without statistical significance. The other meteorological series of the ERA-Interim does not present discrepancies. Only the maximum anomalies of air temperature have significant annual and seasonal positive trends at grid points near the coast of Rio de Janeiro and São Paulo. Despite that the analyses for pressure and wind speed anomalies do not indicate significant trends, they present increases in the interdecadal pattern of the numbers of occurrence of extreme percentiles for almost every grid point. Return levels for 10, 25, 50, 75, and 100 years are estimated at each grid point and many maximum/minimum peaks are close to the return levels for 100-year return periods. The extremal index suggests average cluster sizes associated with no predominance of clustering for the extreme percentiles, which represents weak dependence between the exceedances. These results characterize some independence between extreme meteorological events such as the event that has been taking place in the region. The occurrence of maximum daily wind speed peaks calculated in austral spring, whose values exceeded the previous ones, is identified at three grid points near the southeast Brazilian coast, caused by the passage of the subtropical cyclone “Deni,” which occurred in November 2016.

Extremes, Extremal Index Estimation, Records, Moment Problem for the Pseudo-Lindley Distribution and Applications

The pseudo-Lindley distribution which was introduced in Zeghdoudi and Nedjar (2016) is studied with regards to it upper tail. In that regard, and when the underlying distribution function follows the Pseudo-Lindley law, we investigate the the behavior of its values, the asymptotic normality of the Hill estimator and the double-indexed generalized Hill statistic process (Ngom and Lo, 2016), the asymptotic normality of the records values and the the moment problem.

Clustering of Extremes in Financial Returns: A Study of Developed and Emerging Markets

This paper investigates the clustering or dependency of extremes in financial returns by estimating the extremal index value, in which smaller values of the extremal index correspond to more clustering. We apply the interval estimator method to determine the extremal index for a range of threshold values in the developed and emerging markets from 2007–2017. The indices we used to represent developed markets are from France, Germany, Italy, Japan, USA, UK, Spain, and Sweden. For the emerging markets, we use indices from China, Brazil, India, Malaysia, Russia, Saudi Arabia, and Portugal. The results show that clustering occurs in the emerging and developed markets under several threshold values. This study will shed light on the dependency structure of financial returns data and the proprieties of the extremes returns. Moreover, understanding clustering of extremes in these markets can help investors reduce the exposure to extreme financial events, such as the financial crisis.