Mathematical examination of time series regression, explanation of models and a related application

Time series are used in positive sciences such as mathematics, statistics, physics, in data sets that show increase, decrease, growth, shrinkage depending on time, as well as in social sciences such as finance, banking and econometrics, they are used under many time-related subheadings such as population and stock market. In this study, it is mentioned in which areas time series are used, definitions used in time series are given, an application is made by searching time series regression and ARIMA models in time series. For the time series regression application, the number of midwives in Turkey between the years 1928-2020 was taken from TUIK as annual data. For time series regression, 7 different models were applied to the data and the best model was found. For this model, prediction values were obtained for the years 2021 and 2022. In the application made by using the air quality index data taken daily in 2014, ARIMA models were applied to the data. Since the data are taken on a daily basis, the estimation values are calculated for January 2015. First of all, it was checked whether the series contains seasonality and whether it is stationary. Necessary analyzes were made and as a result, it was seen that the series did not contain seasonality and that the series was stationary at the level. Modeling was done by deciding that the most suitable ARIMA model for the data set is the ARMA(p,q) model, since the series is not a seasonal series and is stationary at the level. The best model was selected among the models, and the prediction values for January 2015 were found and the predicted values were evaluated according to the EPA air quality index table.