D. B. Rogdestvenskii

Extrapolation methods at the decision of problems of forecasting are developed for that simple reason, that become standard the approach of mathematical modelling already throughout many decades suffers failure. The reason of these failures consists basically in ignorance of a subject of modelling. The methods of extrapolation existing already throughout considerable time, are applicable to signals with the limited spectrum, that, generally speaking, it is not meaningful. Extrapolation has practical and reasonable sense for the signals limited in time, i.e. for signals with an infinite spectrum. Real processes can be presented functions which are continuous also which, it is possible to consider, have the limited spectrum. However, observable processes are limited to an interval of supervision and it is necessary to represent them in the form of product of the process on the rectangular function having an infinite spectrum. The idea of working out of algorithm of extrapolation is put in suppression of the distortions connected with the phenomena accompanied processes of digitization and limitlessness of a spectrum of investigated process. The method of extrapolation of discrete process is based on its restoration in continuous process. Use of the discrete form of integrated Fourier transformation has appeared the most attractive. Its analogue is the truncated Kotelnikov series. An essential element, a positive role in the decision of a problem of extrapolation, introduction of allocating function instead of the mentioned rectangular function is played. Allocating function exists in infinite limits in time and has the limited spectrum. Introduction of this function has allowed to use methods, suitable for the signals limited on a spectrum. Methods of synthesis of digital filters of low frequencies are developed for realisation of measures on ordering of a spectrum of initial process. In article the considerable material of practical application of the developed methods is presented at the decision of problems of processing the forecast of some geophysical characteristics. Long time numbers of measurements of land temperature, level of Caspian sea concern them. The analysis of results of measurement of ecological conditions in a zone of work of the industrial enterprise for destruction of poison gases is carried out. Extrapolation methods possess some advantages before mathematical modelling. They possess properties of universality, and can be applied to the decision of many problems where forecast definition is required. The science concerns one of such sciences about management. The forecasting method is the basic management method, however, managers try to bypass discussion of a question of forecasting in management problems. Use of mathematical modelling does not solve a management problem as mathematical modelling is ineffective at the decision of a problem of the forecast. The offered methods of extrapolation presented in article can find application in management problems