Modification Parameter Estimation of the Seasonal Autoregressive Moving Average Process in the Present of Arm (1, 1)

Error was known to be persistent in the measurement of parameters. This research work investigated seasonal autoregressive integrated moving averages with time series error patterns (SARIMA-E). The study enhances the minimized effect and improves the model resolutions. (SARIMA-E) with auto-regressive moving average error ARMA(1,1) is considered using the maximum likelihood method, iteration procedure, and chi-square test. However, the result shows that the optimum model is very significant. Furthermore, the forecast performance measurement and properties of errors with different values of parameters were investigated and analyzed. The test of the seasonal unit root was observed in both cases and the simulations were conducted using R - statistical software and monthly Temperature real data obtained for the period between 1988 2022 in Zamfara was equally used to validate the results. Finally, the research finding depicts that the result obtained was too close to the parameter values of the model analytical results obtained and presented. It was suggested that these results would be useful in predicting the stability of the system.