Grey modeling method for estimating time series

Grey systems theory predicts the behavior of unknown systems with little data. Grey prediction theory is an interdisciplinary scientific field and has been applied to many systems with partially unknown parameters over the past three decades. In this study, Turkey's R&D and education expenditures data between 2011-2020 and electricity production data between 2010-2019 were taken from the Turkish Statistical Institute. R&D and education expenditures for the years 2021-2030 and electricity production for the years 2020-2029 were estimated by using Standard Grey Model (GM (1,1)), Novel Grey Model (NGM(1,1)) and Exponential Grey Model (EXGM (1,1)). The results of all three models were compared. The percentage relative error (RPE) between the actual and predicted values and mean absolute percentage error (MAPE) were determined. The correlation between the actual value and the predicted value was examined. The MAPE value for R&D expenditures was calculated as 2.95% with GM (1,1), 14.01% with NGM (1,1) and 1.48% with EXGM (1,1), respectively. It was calculated as 3.32% with GM (1,1), 8.66% with NGM (1,1) and 3.09% with EXGM (1,1) for education expenditures. It was calculated as 1.58% with GM (1.1), 8.66% with NGM (1,1) and 1.36% with EXGM (1,1) for electricity production. R2 values, which show the correlation between actual value and estimated value were calculated as 0,9974 with GM (1,1), 0,9821 with NGM (1,1) and 0,9985 with EXGM (1,1) for R&D expenditures. It was calculated as 0,9845 with GM(1,1), 0,9619 with NGM (1,1) and 0,9846 with EXGM (1,1) for education expenditures. For electricity production, it was calculated as 0,9734 with GM (1,1), 0,9619 with NGM (1,1) and 0,9753 with EXGM (1,1). As a result, when the error and correlation results of the estimation values obtained from GM (1,1), NGM (1,1) and EXGM (1,1) methods are examined, it was seen that the EXGM (1.1) method gives better results in all applications. It was predicted that our country's R&D and education expenditures and electricity production will increase exponentially in the next 10 years.