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We consider the problem of the annual mean temperature prediction. The yearstaken into account and the corresponding annual mean temperatures are denotedby $0,\ldots, n$ and $t_0$, $\ldots$, $t_n$, respectively. We propose topredict the temperature $t_{n+1}$ using the data $t_0$, $\ldots$, $t_n$. Foreach $0\leq l\leq n$ and each parametrization $\Theta^{(l)}$ of the Euclideanspace $\mathbb{R}^{l+1}$ we construct a list of weights for the data$\{t_0,\ldots, t_l\}$ based on the rows of $\Theta^{(l)}$ which are correlatedwith the constant trend. Using these weights we define a list of predictors of$t_{l+1}$ from the data $t_0$, $\ldots$, $t_l$. We analyse how theparametrization affects the prediction, and provide three optimality criteriafor the selection of weights and parametrization. We illustrate our results forthe annual mean temperature of France and Morocco.

Parametrizations, weights, and optimal prediction: Part 1