Forecasting the population of Türkiye using GM (1,1) models

In this study, Türkiye's population is estimated for the period until 2050 using the 2007-2022 address-based censuses. The five different Grey models are used for estimating it. These models are given by Grey Standard GM (1,1), Grey Time-Varying Dynamic, Grey Gompertz, Grey Verhulst and Grey Exponential forecasting models, respectively. Comparison of the models is evaluated by Mean Absolute Percentage Error (MAPE), Regression Coefficient (R2), Variance Ratio (C) and Error Probability (P) criteria, respectively. The Grey Gompertz was determined as the most suitable model with a value of 0.12788% according to the MAPE criterion and a value of 0.99898 according to the R2 criterion for the years 2007-2022; According to criterion C, Grey Time- Varying Dynamic was determined as the most appropriate model with a value of 0.02286. According to the P criterion, all models were equal to 1. The forecast results for 2023-2050 are obtained by the five grey models and compared with the forecast values shared by TUIK in 2018. Accordingly, the Grey Gompertz was identified by the most compatible model with TUIK estimates with a value of 0.68116% according to the MAPE criterion and a value of 0.05218 according to the C criterion. According to the R2 criterion, the Grey Verhulst gave the most compatible value with a value of 0.99818. The population of Türkiye will be 105,948,975 based on the Grey Gompertz model, 106,877,632 based on the Grey Time-Varying Dynamic model, and 102,591,471 based on the Grey Verhulst model by 2050.