Trend detection for heteroscedastic extremes

Modeling space-time trends and dependence in extreme precipitations of Burkina Faso by the approach of the Peaks-Over-Threshold

“…In this study we proposed a new flexible methodology for trend detection in the extremes capable of capturing marginal non-stationarities and the dependence structure between margins using generalized -Pareto processes. We computed the non-stationary return ii) The result (19) is shown in a similar way B Asymptotic distribution of -Pareto Process…”

“…In the framework of the model ( 9), Mefleh et al [19] shows that the empirical point measure converges in distribution in the space of point measure M p = M p ([0, 1] × (0, ∞]) to a Poisson point process with intensity measure c(u)duγz −(γ+1) dz on [0, 1] × (0, ∞]. In such a case the times of exceedances for high threshold x and the value of exceedances are asymptotically independent with distributions respectively equal to the trend density function c θ (u, s), s ∈ S and the Pareto distribution of tail index γ.…”

“…From a statistical point of view, the hypothesis of stationarity becomes untenable and debatable, and thus raises the question of detecting trends in extreme events, which has been the subject of much attention over the last 30 years. The classical Theory of Extreme Values extended both to non-stationary and non-independent observations provides a rigorous mathematical framework to deal with this question of trend detection in extremes ( [13], [16], [19], [5]).…”

Space-Time Trend Detection and Dependence Modeling in Extreme Event Approaches by Functional Peaks-Over-Thresholds: Application to Precipitation in Burkina Faso

“…e skedasis function describes the evolution of extreme events jointly in space and time. In the framework of the model (1), Mefleh et al [8] shows that the empirical point measure converges in distribution in the space of point measure M p � M p ([0, 1] × t(0, ∞]) to a Poisson point process with intensity measure c(u)ducz − (c+1) dz on [0, 1] × (0, ∞). In this case, the times of exceedances for high threshold x and the value of exceedances are asymptotically independent with distributions respectively equal to the trend density function c θ (u, s), s ∈ S and the Pareto distribution of tail index c.…”

“…From a statistical point of view, this raises the question of trend detection in extreme events. e classical extreme value theory extended both to nonstationary and non-independent observations provides a rigorous mathematical framework to deal with this question of trend detection in extremes [5][6][7][8]. is issue was rst generally studied in extreme value literature by parametric pointwise approaches in which an extreme value model (GEV or GPD) is tted to the data at each site in turn, leaving the parameters of the marginal distributions to evolve with time or other significant covariates [9][10][11][12][13].…”