Statistical Prediction (No. 18)

Abstract

The first attempts at the statistical prediction of future values of certain meteorological parameters using linear regression equations to give a future value of the quantity Ay of interest in the form of a simple linear combination of the △x ₁,… △x _k known from observations made in the past or present were started in the 1920’s. (In addition to Bauer’s paper of 1925 referred to by A.N. Kolmogorov, we can also refer to later works [1]–[6] containing a number of additional references.) At first sight this prediction method seems to be quite simple: it requires only preliminary estimates of a certain number of correlation coefficients which determine the unknown coefficients a ₁,…, a _k in the regression equations and does not require cumbersome calculations such as those involved in “dynamic weather forecasting” based on numerical solution of partial differential equations approximately describing the dynamics of the atmosphere. Here, the only problem is to choose appropriate predictors △x ₁,…, △x _k , that is, atmospheric characteristics in the past and present whose values are used for predicting Ay. It turns out, however, that to choose appropriate predictors is not that simple.