A new method for estimating the forecast quality with consideration for the errors of calculating the unknown parameters

In this study, the problem of estimating the forecast accuracy of a model is considered. A widespread practice is to approximate the population expectation of the forecast accuracy by the sample expectation, which is equivalent to the uniform consideration for the deviations of the forecast from the exact value of a quantity for all time moments. If the vector of unknown parameters is estimated at each step only from the preceding observations, the significance of the deviations is not the same at all time moments. In this study, we propose a method that takes into account the forecast errors with different weights. The problem of constructing the most accurate estimate of the forecast quality, a parameter from which the condition for the optimal weights can be derived, is formalized. Monte-Carlo experiments are used to compare the accuracy of the methods for estimating the forecast quality in the cases when the observations are taken into account with the same weights, with optimum weights, and with the weights calculated using a numerical procedure.