Parameter Estimated of Seasonal Auto-regressive Integrated Moving Average Model with AR(1) Error Process

From the previous literature, there had been various research on models with error processes especially, the time series model with corrupted error processes. The gap to be filled here was the extension of such a model to the SARIMA model with corruption error processes. Thus, this research work focused on parameter estimates with a corrupted AR(1)error process. Auto-covariance functions were used to estimate the variances of error terms that characterized the SARIMA model. The forecast performance measurement was investigated and properties of errors with different values of parameters were examined. A test of seasonal unit root was carried out and the result revealed a seasonality effect. Simulation with R Statistical software was used to prove the findings. In addition, the monthly temperature data of Zamfara State from 1998 to 2020 was used to validate the results using the iteration procedure and chi-square statistic.The results from the study showed that the research findings were very significant to the error process and would be useful to researchers in the prediction and handling of natural calamities.