DEVELOPMENT OF SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL WITH ERROR PROCESS

This research work investigated with error process. The auto covariance function maximum likelihood methods, iterative method and chi-squares test statistics is used to develop SARIMA model corrupted with error process that is used to estimate the true parameter of the SARIMA model. The forecast performance measurement and properties of error with different value are also investigated. Test of seasonal unit roots are also carried out in the work. The simulation, and real data of Zamfara state monthly Rain fall from 1998 to 2022 is used to validate the results with  R - Statistical software version 4.1.1 and mini tab statistical software version 14. The result showed a significance p- value of 0.000, the proposed model provides a generalization and more flexible specification than the existing models of AR (1) error and ARMA (1,1) error in fitting time series processes in the presence of errors . Hence, the studies showed that, the finding is closely to the true parameter of the process and would be useful to researchers in the prediction and handling of natural calamities that disturb the otherwise stability of a system.