Abstract. The paper considers a problem of extrapolating functions of several variables. It is assumed that the values of the function of m variables at a finite number of points in some domain D of the m-dimensional space are given. It is required to restore the value of the function at points outside the domain D. The paper proposes a fundamentally new method for functions of several variables extrapolation. In the presented paper, the method of extrapolating a function of many variables developed by us uses the interpolation scheme of metric analysis. To solve the extrapolation problem, a scheme based on metric analysis methods is proposed. This scheme consists of two stages. In the first stage, using the metric analysis, the function is interpolated to the points of the domain D belonging to the segment of the straight line connecting the center of the domain D with the point M, in which it is necessary to restore the value of the function. In the second stage, based on the auto regression model and metric analysis, the function values are predicted along the above straight-line segment beyond the domain D up to the point M. The presented numerical example demonstrates the efficiency of the method under consideration.

Interpolation and forecasting schemes are derived in the frame of the metric analysis method for time series described by functions of several variables. The efficiency and reliability of the proposed approach are illustrated on case study problems.

One of the primary goals of data processing is the problem of interpolation of the values of investigated function. Different methods and schemes for the solving various interpolation problems are developed and in use [1-3]. The schemes of metric analysis for restoration of function of one and many variables are also in use [4-9]. The new approach for one dimensional and multidimensional interpolation, named by authors "metric analysis", and the algorithms based on this approach are offered. It is shown that the metric analysis interpolates multidimensional functions with high accuracy, even in the case of a small number of points in which values of the function are defined (interpolation knots).

One of primary goals of data processing is the problem of forecasting of investigated function values. Different methods and schemes for solving forecasting problems are developed and in use [1, 2, 4, 8, 11]. In this paper it is used the method, named by authors metric analysis. New forecasting algorithms are developed based on metric analysis [5-7, 9, 10]. It is shown that the metric analysis solves the problem of forecasting of functional values with high accuracy.