Parametrizations, weights, and optimal prediction: Part 1
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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,..., n and t_0, ..., t_n, respectively. We propose to predict the temperature t_n+1 using the data t_0, ..., t_n. For each 0≤ l≤ n and each parametrization Θ^(l) of the Euclidean space R^l+1 we construct a list of weights for the data {t_0,..., t_l} based on the rows of Θ^(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, ..., 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.
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