Akademik Veri Yönetim Sistemi
ICPAM VAN 2022 4th International Conference on Pure and Applied Mathematics, Van, Türkiye, 22 - 23 Haziran 2022, ss.96
Grey system theory was introduced to find solutions to problems involving small sample and weak
information. Its application areas have five components, namely Grey relational analysis (GRA),
Grey modelling, Gray prediction, Grey control and Grey decision making. In the process of creating
the grey prediction model, the original data is accumulated into a new data column with strong
regularity and a new model is created. Then, the reduction model is created from this new data
column by inverse operation and the final prediction model is obtained. The GM(1,1) model is the
most widely used grey forecasting model. The grey model was developed to make inferences for
future periods and to predict them based on the values of data from past periods. Today, many
quantitative techniques are used for the estimation of time series. However, the important thing
here is to keep the error rates that occur as a result of the predictions made by the techniques at a
minimum level. In this sense, sometimes by modifying the error terms and sometimes by combining
different techniques, it is tried to reduce the error rates and to obtain more accurate estimations.
Because the plans made for the future and the policies that can be determined gain meaning only
with these predictions. The lower the error rate, the higher the performance of the prediction model
will be. With these in mind, GM(1,1) is one of the most commonly used Grey forecasting models.
This model is a time series prediction model consisting of first order differential equations. The
minimum number of data should be four to create the GM(1,1) model. In general, GM(n,m) refers
to the grey model. n is the number of nth order differential equations, m is the number of variables.