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Tomsk state university (Tomsk)
The task of construction of a recurrent forecasting filter of time series is considered. For solution the theory of spline-schemes, precise on polynomials is used. The recursion formula of calculation of coefficients of B-splines of the third degree on values of a given function in knots of an even grid is represented. It is supposed, that the function presets with an error and that the knots of a spline are allocated through m points of the definition of the function.
The theorem of scheme exactness on polynomoals of the third degree, asymptotic stability and unbiasednesses of resulting spline approximation is proved. Are given results of numerical experiments.
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