Title: Parametrizations, weights, and optimal prediction: Part 1,
Abstract: We consider the problem of the annual mean temperature prediction. The years
taken into account and the corresponding annual mean temperatures are denoted
by $0,\ldots, n$ and $t_0$, $\ldots$, $t_n$, respectively. We propose to
predict the temperature $t_{n+1}$ using the data $t_0$, $\ldots$, $t_n$. For
each $0\leq l\leq n$ and each parametrization $\Theta^{(l)}$ of the Euclidean
space $\mathbb{R}^{l+1}$ we construct a list of weights for the data
$\{t_0,\ldots, t_l\}$ based on the rows of $\Theta^{(l)}$ which are correlated
with 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 the
parametrization affects the prediction, and provide three optimality criteria
for the selection of weights and parametrization. We illustrate our results for
the annual mean temperature of France and Morocco.