Modeling of air temperatures: preprocessing and trends, reduced stationary process, extremes, simulation

Dacunha-Castelle, Didier; Hoang, Thi Thu Huong; Parey, Sylvie

Journal de la société française de statistique, Tome 156 (2015) no. 1, pp. 138-168.

Notre premier objectif est de donner une méthodologie complète pour obtenir un modèle de simulation valable pour un très grand nombre de séries de température de l’air . Simulateurs existants ont très bonnes propriétés pour l’essentiel de la distribution, mais ils sont incapables de se reproduire valeurs extrêmes ainsi que les vagues de froid ou de chaud. Ainsi, nous nous concentrons sur cet aspect afin de couvrir à la fois l’essentiel des données et les valeurs extrêmes.

D’abord, nous donnons quelques résultats nouveaux sur prétraitement ( la phase au cours de laquelle les tendances et saisonnalités sont supprimés ) . Dans ce contexte, le choix des tendances non paramétriques nécessite de nouveaux résultats sur la validation croisée . Une fois additifs (moyenne) et multiplicatif ( variance) Tendances et saisonnalité sont supprimés, nous testons la cyclo- stationnarité de la série réduite . Dans presque tous les cas , il ne reste aucune tendance , même pour les valeurs extrêmes .

Pour modéliser les observations , nous commençons à partir des estimations non paramétriques de l’ espérance et la variance d’une journée conditionnel à la précédente et à partir des études de corrélations . La meilleure classe de modèle semble la classe Farch saison . Puis, des améliorations mathématiques supportées par les physiques , procédé Farch est interprété comme le schéma d’Euler des diffusions en temps continu , et donc que les modèles mal spécifiés et modifiés par la troncature adaptative des innovations en utilisant de nouveaux résultats de la théorie sur les diffusions extrême . Ces résultats sont branchés sur la probabilité des processus Farch pour obtenir une estimation pratique.

Nous détaillons certains résultats de l’application d’ environ 200 stations d’Eurasie et aux états-Unis , y compris les procédures de validation du modèle. La comparaison de certains modèles existants est également envisagée.

Our first goal is to give a complete methodology to get a simulation model valid for a very large number of air temperature series. Existing simulators have quite good properties for the bulk of the distribution but they are unable to reproduce extreme values as well as cold or hot waves. Thus we focus on this aspect in order to cover both the bulk of the data and extreme values.

First we give some new results on preprocessing (the phase during which trends and seasonalities are removed). In this context, the choice of non parametric trends requires some new results on cross validation. Once additive (mean) and multiplicative (variance) trends and seasonality are suppressed, we test the cyclo-stationarity of the reduced series. In almost all cases, there does not remain any trend even for extremes values.

To model the observations, we start from non parametric estimates of the expectation and variance from a day conditional to the previous one and from studies of correlations. The best class of model seems the seasonal FARCH class. Then for mathematical improvements supported by physical ones, FARCH process is interpreted as the Euler scheme of continuous-time diffusions and thus as misspecified models and modified by adaptive truncation of innovations using new results of extreme theory on diffusions. These results are plugged in the likelihood of FARCH processes to get a convenient estimation.

We detail some results of the application to about 200 stations from Eurasia and United States, including the validation procedures for the model. The comparison to some existing models is also considered

Keywords: temperature, time series, preprocessing, cyclo-stationarity, extremes, diffusion, simulation model
Mot clés : température, série temporelle, pretraitement, cyclo-stationnarité, extrêmes, diffusion, modèle de simulation

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