Time series have gained great importance and have been applied in a manner in the economic, financial, health and social fields and used in the analysis through studying the changes and forecasting the future of the phenomenon. One of the most important models of the black box is the "ARMAX" model, which is a mixed model consisting of self-regression with moving averages with external inputs. It consists of several stages, namely determining the rank of the model and the process of estimating the parameters of the model and then the prediction process to know the amount of compensation granted to workers in the future in order to fulfil the future obligations of the Fund. , And using the regular least squares method and the frequency squares method by "Kalman filter" and "forgetting factor" to obtain the best predictable way for the future using data from the Social Security Department for workers and from the period 1/2013 to 6/2019 where The method of least squares "OLS" was compared with the method of iterative least squares "RLS" by "Karman Filter" and found that "OLS" method is the best according to the comparison measures "RMSE, MAPE" and it gave accurate results close to the real values
