Forecasting with Markovian max-stable fields in space and time: An application to wind gust speeds

TL;DR

This paper introduces a novel space-time max-stable model with a max-autoregressive structure for forecasting wind gust speeds, demonstrating its effectiveness on French data and establishing its theoretical properties.

Contribution

It develops a new max-autoregressive model with advection for space-time max-stable fields, suitable for forecasting atmospheric variables, and proves its statistical properties.

Findings

The model accurately forecasts wind gusts in France.

It outperforms existing competitor models.

Theoretical properties like consistency and asymptotic normality are established.

Abstract

Hourly maxima of 3-second wind gust speeds are prominent indicators of the severity of wind storms, and accurately forecasting them is thus essential for populations, civil authorities and insurance companies. Space-time max-stable models appear as natural candidates for this, but those explored so far are not suited for forecasting and, more generally, the forecasting literature for max-stable fields is limited. To fill this gap, we consider a specific space-time max-stable model, more precisely a max-autoregressive model with advection, that is well-adapted to model and forecast atmospheric variables. We apply it, as well as our related forecasting strategy, to reanalysis 3-second wind gust data for France in 1999, and show good performance compared to a competitor model. On top of demonstrating the practical relevance of our model, we meticulously study its theoretical properties and show the consistency and asymptotic normality of the space-time pairwise likelihood estimator which is used to calibrate the model.