In statistics, extreme events are often defined as excesses above a given large threshold. This definition allows hydrologists and flood planners to apply Extreme‐Value Theory (EVT) to their time series of interest. Even in the stationary univariate context, this approach has at least two main drawbacks. First, working with excesses implies that a lot of observations (those below the chosen threshold) are completely disregarded. The range of precipitation is artificially shopped down into two pieces, namely large intensities and the rest, which necessarily imposes different statistical models for each piece. Second, this strategy raises a nontrivial and very practical difficultly: how to choose the optimal threshold which correctly discriminates between low and heavy rainfall intensities. To address these issues, we propose a statistical model in which EVT results apply not only to heavy, but also to low precipitation amounts (zeros excluded). Our model is in compliance with EVT on both ends of the spectrum and allows a smooth transition between the two tails, while keeping a low number of parameters. In terms of inference, we have implemented and tested two classical methods of estimation: likelihood maximization and probability weighed moments. Last but not least, there is no need to choose a threshold to define low and high excesses. The performance and flexibility of this approach are illustrated on simulated and hourly precipitation recorded in Lyon, France.

Genton et al. (2011) investigated the gain in efficiency when triplewise, rather than pairwise, likelihood is used to fit the popular Smith max-stable model for spatial extremes. We generalize their results to the Brown–Resnick model and show that the efficiency gain is substantial only for very smooth processes, which are generally unrealistic in applications.

Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that exhibit a property known as asymptotic independence. However, weakening dependence does not automatically imply asymptotic independence, and whether the process is truly asymptotically (in)dependent is usually far from clear. The distinction is key as it can have a large impact upon extrapolation, that is, the estimated probabilities of events more extreme than those observed. In this work, we present a single spatial model that is able to capture both dependence classes in a parsimonious manner, and with a smooth transition between the two cases. The model covers a wide range of possibilities from asymptotic independence through to complete dependence, and permits weakening dependence of extremes even under asymptotic dependence. Censored likelihood-based inference for the implied copula is feasible in moderate dimensions due to closed-form margins. The model is applied to oceanographic datasets with ambiguous true limiting dependence structure. Supplementary materials for this article are available online.

Smart electricity meters are currently deployed in millions of households to collect detailed individual electricity consumption data. Compared with traditional electricity data based on aggregated consumption, smart meter data are much more volatile and less predictable. There is a need within the energy industry for probabilistic forecasts of household electricity consumption to quantify the uncertainty of future electricity demand in order to undertake appropriate planning of generation and distribution. We propose to estimate an additive quantile regression model for a set of quantiles of the future distribution using a boosting procedure. By doing so, we can benefit from flexible and interpretable models, which include an automatic variable selection. We compare our approach with three benchmark methods on both aggregated and disaggregated scales using a smart meter data set collected from 3639 households in Ireland at 30-min intervals over a period of 1.5 years. The empirical results demonstrate that our approach based on quantile regression provides better forecast accuracy for disaggregated demand, while the traditional approach based on a normality assumption (possibly after an appropriate Box-Cox transformation) is a better approximation for aggregated demand. These results are particularly useful since more energy data will become available at the disaggregated level in the future.