Finite Differences Method for Socio-Economic Modeling

In the issue we consider socio-economic processes modeling based on first and second order finite differences models. Since commonly used modeling methods have drawbacks and thus are not universal it was necessary to develop alternative methods which are better in some aspects. Specifically multiple linear regression models have limited prediction abilities, and differential regression coefficient evaluation method is quite complex and have some economically uninterpreted excess tunings. In our research we replaced first and second order derivatives in differential regression models with their finite differences equivalents and thus gained a multiple linear regression model modification which includes first and second order auto regression items. Estimation of their parameters can be done using a modification of least-squares method in which we demand that factor coefficients signs for models with and without auto regression items are the same. Due to additional items in the modified linear regression models their approximation capacity is greater than of a common model. However for application purposes model forecasting capacity is more important, i.e. the forecasting efficiency criterion is the most significant for a decision making. In order to estimate forecasting potential of modified multiple linear regression models we performed coefficient estimation of unmodified and modified equations for 59 various socio-economic data sets. We used shortened time series, so we could calculate model values and compare them to actual data. It was determined that modified multiple linear regression models allowed to make better predictions in 49 (76.3 %) cases. We can now assume that addition of auto regression items into multiple linear regression model can increase short-term forecasting efficiency.