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The regression forecasting models are often used at realization of forecasting in economic and social spheres. Ability of regression equation to represent interrelation between phenomena has found practical application in the forecasting analysis.
Today forecasting is connecting with a lot of difficulties. Therefore the purpose of this work is development of new and efficient methods that increase accuracy of forecasting.
For achievement of delivered goal it is necessary to solve following problems:
- to consider 3 methods that increase accuracy of forecasting with application forecasting model on basis of pair linear regression and determine what parameters of basic statistical data is defined the choice of this or that method;
– to find the parameters of methods which permit to maximize "gain" from their application.
It was conducted and conducting now many researches connected with forecasting, including masters DonNTU. However methods which will be considered in this work are new and were not used earlier. The theme of master's work "Investigation of increase accuracy regression models methods" (master Scherbak I. V.) is the most close to my theme of master's work.
There are many books all over the world which devoted to forecasting. In Ukraine it, for example, the book "Statistical modelling and forecasting", which author is Erina A. M. (Kiev national economic university).
From the books written in Russia I should note the book "Mathematical methods of construction of forecast", authors are Greshilov A. A., Stakun V. A., Stakun A. A. (Moscow).
There is special journal devoted to forecasting "International Journal of Forecasting" edited by R. J. Hyndman.
Also a lot of systems (programs) for forecasting are exist. The main of which:
1) System STATISTICA (www.statsoft.com). The producer company is StatSoft Inc.
2) System Forecast Pro (www.forecastpro.com). Headquartered in Belmont, Massachusetts, BFS was co-founded by Dr. Robert (Bob) Goodrich and Eric Stellwagen and is privately held. Founded in 1986, Business Forecast Systems, Inc. (BFS), is the maker of Forecast Pro, the leading software solution for business forecasting, and is a premier provider of forecasting education.
3)Package STATPRO (www.icm.by/public/developments/p141/indexr.html) (Belarussian state university)
4) Program for forecasting from site http://forecasting.ikernel.org
5 Program Excel-forecast (http://Excelprognoz.narod.ru)
In this work are considered three methods of increase accuracy of forecasting.
The first method consists in a finding linear regression equation on initial statistical data, which parameters are defined by means of least-squares method and displacement of this equation concerning initial one on value  . So you have corridor in which do not get heterogeneous points.
Example. Statement of problem: N= 20points, expectancy of hitting regression data to interval R=0,8,  ,  .
If we used by first method, then we get following figure (Fig. 1)
Fig.1 - The first method
The second method consists in finding linear regression equation, the mean value of regressor and dropping a perpendicular in point xm (mean value x). After that we plot two straight lines with displacement on value , place in parallel with perpendicular. For our example we will have (Fig. 2):
Fig.2 - The second method
The third method consists in a combination of use of first and second methods. It is necessary to consider in order to general expectancy of hitting in a rectangular corridor was equal 0,8, it is necessary to take probabilities equal 0,89. The result of use the third method represent by diagram 3.
Fig.3 - The third method
(Animated image consist of 11 frames, 12 cycles)
Measure of efficiency:
where
λ – value of displacement;
tα, tα'– confidence interval for initial data and data after casting-out.
There are results of spent researches on diagrams 4 and 5.
Fig.4 - "Gain" of 1-st method
Fig.5 - "Gain" of 2-nd method
Under corresponding values of parameters , , m1 the "gain" under has made 85% that corresponds to casting-out 40% of initial data.
All three methods are intended for casting-out heterogeneous data. If considerable dispersion on y, then reasonable to use the 1st method, if on x than the 2nd, under equal dispersion on x and y – the 3rd.
The casting-out heterogeneous data when you use any of three methods brings about "gain".
The value of "gain" has a maximum which value depends from  ,  , Rxy
This methods approach for any symmetric distributions of data concerning regression equation.
The considered methods can be used for a case nonlinear regression models, if this models are reduced to linear.
Literature
1) Четыркин Е.М. Статистические методы прогнозирования. Изд. 2-е, перераб. и доп. М., "Статистика", 1997
2) Колемаев В.А. Эконометрика: Учебник. – М.: ИНФРА-М, 2004 – 160 с.
3) Айвазян С.А., Мхитарян В.С. Прикладная статистика и основы эконометрики. – М.: ЮНИТИ, 1998.
4) Єріна А. М. Статистичне моделювання та прогнозування: Навч. посібник - К.: КНЕУ, 2001 - 170 с. http://www.gmdh.net/articles/theory/StatModeling.pdf
5)Грешилов А. А., Стакун В. А., Стакун А. А. Математические методы построения прогнозов. - М.: Радио и связь, 1997 - 112 с. http://www.gmdh.net/articles/theory/TimeSeries.pdf
6) Орлов А.И. Прикладная статистика. Учебник. - М.: Издательство «Экзамен», 2004. - 656 с.
7) Green W. H. Econometric analysis: 4th ed. - N. Y.: Macmillan Publishing Company, 2000
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