V.T. Sarychev

The work purpose is creation of algorithm of the spectral estimation, allowing to extrapolate initial data far beyond a watch window. Not any process allows to prolong the limited numbers representing it. The processes essentially different from noise possess such properties only. As a measure of such difference it is offered to use Kullback information. Process corresponding to numbers, is represented by ensemble of harmonious fluctuations. The ensemble condition is described by function of frequency distribution of oscillations (FFDO). Complex spectrum (CS), entropy and the information are defined by corresponding functional of FFDO. The parametrical form of FFDO is defined by the maximum-entropy criterion. Values of the parametres are estimated by a method coordinate-wise descent to a minimum functional of root-mean-square deviation between an initial data and the numbers received by inverse Fourier transform of CS. Besides, values of the parametres should be such that the Kullback information was whenever possible maximum. CS it is defined by the moment of the first order complex amplitude of FFDO. If the signal contains the spectral lines, which width less than inverse value of duration of a watch window the algorithm allows to make a main lobe corresponding to these lines in a spectrum estimation narrow, and level of lateral lobe to make disappearing small. This property of algorithm allows to use it for extrapolation of initial data. Testing and check of possibilities of algorithm was spent for harmonious oscillation and the mid-annual Wolf numbers. The Kullback information of a harmonious signal reached values 13.8. The further increase of the information was limited to technical possibilities of the computer. (Even at calculations with double accuracy there was an order overflow). The harmonious fluctuation presented by three hundred value was prolonged on 1000 readout forward and back. Thus phase distortion degree shares, and amplitude distortions made some percent beoynd a watch window. Amplitude distortions with good accuracy submitted to the linear law. At the account of this law accuracy of approximation made ~ 0.01 %. At estimation CS of the mid-annual Wolf numbers an initial data was preliminary transformed to a sign-variable number: values of the Wolf numbers of odd cycles of the Sun activity undertook with a negative sign whereas in even its undertook without change, i.e. with a plus. This preliminary processing has allowed to «impoverish» a spectrum essentially. In a spectrum it has appeared only seven lines which energy exceeds one percent. The periods of fluctuations corresponding to these lines, lie in the range from 13 till 26 years. 70 % of energy are concentrated in a lobe of the spectrum corresponding to the period of 22.19 years. The lobe with the period of 18 years is answered with 12 % of energy. At duration of calculations one month on the personal computer with clock frequency of 3 GHz was possible to finish value of the information of Kulbaka to 5.2. Accuracy of approximation of an initial data by inverse Fourier transform of CS made 0.002 %. Results of extrapolation of a number on an interval from 1100 till 2600 years are resulted.