Parametrizations, weights, and optimal prediction: Part 1

TL;DR

This paper introduces a new framework for predicting annual mean temperatures using parametrizations and weights, analyzing their impact on prediction accuracy with applications to France and Morocco.

Contribution

It proposes a novel method for temperature prediction based on parametrizations and optimal weight selection, with three criteria for optimality and real-world temperature data applications.

Findings

Parametrization significantly influences prediction accuracy.

Optimal weight selection improves temperature forecasts.

Method applied successfully to France and Morocco temperature data.

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.