تشخيص وتقدير نماذج السلاسل الزمنية الموسمية مع تطبيق عملي

Diagnosis and estimation of seasonal time-series models with practical application

In this thesis, the series of daily temperatures recorded in the center of Hilla District / Babylon Governorate for the year (2020), which included (334) observations, which were obtained from the Iraqi Meteorological Authority, was analyzed using autoregressive models of seasonal moving averages SARIMA and autoregressive models of multiple moving averages. Seasonality based on ready-made programs (Minitab 17, Matlab 2015, E-views 10) with the aim of diagnosing the best seasonal model for the time series from a set of models that have been reconciled, and then choosing the best model from these models using the comparison criteria between models (AIC, BIC, SMAIC). ) And then estimating the diagnosed model using three methods of estimation, which are the approximate maximum possibility method, the exact maximum possibility method, and the nonlinear least squares method, and then comparing these methods using the statistical criterion, the mean squares of error, to reach the best one. And then compare the method of artificial neural networks with the rest of the methods. It was concluded that the doubled seasonal model ARIMA(p,q,d)x(P,Q,D)2 as a representative model for the seasonal time series under study, as well as the multiple seasonal model of the rank ARIMA(1,1,0)x(1 ,2,0)2 as the best seasonal model for the temperature series. The approximate maximum possibility method outperformed the exact maximum possibility method and the nonlinear least squares method in estimating the parameters of the multiplicative seasonal model ARIMA(1,1,0)x(1,2,0)2. It has been shown that the artificial neural networks method is better than the rest of the estimation methods based on the MSE standard.