Objectives: This study aims to provide statistical information summarizing the general structure about the effects and process of infection in all countries of the world in the light of the data obtained and to model the daily change of infection criteria. Methods: The number of COVID 19 epidemic cases of Turkey and the selected G8 countries, Germany, United Kingdom, France, Italy, Russia, Canada, Japan between 1/22/2020 and 3/22/2020 has been estimated and forecasted in this study by using some curve estimation models, Box-Jenkins (ARIMA) and Brown/Holt linear exponential smoothing methods. Results: Japan (Holt Model), Germany (ARIMA (1,4.0)) and France (ARIMA (0,1,3)) provide statistically significant but clinically unqualified results in this data set. UK (Holt Model), Canada (Holt Model), Italy (Holt Model), Turkey (ARIMA (1,4,0)) and Russia?? the results are more reliable. This is specified for the particular model used in this case Turkey. Conclusion: Certainly, more accurate evaluations can be made with more data in future studies. Nevertheless, since this study provides information about the levels at which the number of cases may extend in case that the current situation is not intervened, it can guide countries to take the necessary measures and to intervene it earlier.