Generalised space-time seasonal autoregressive integrated moving average seemingly unrelated regression modelling of seasonal and non-stationary data

The Generalised Space-Time Seasonal Autoregressive Integrated Moving Average (GSTSARIMA) model is known to efficiently handle non-stationary and seasonal data. The single equation model might be insufficient to capture relationships between or among response variables. The joint modelling of response variables is necessary for nonstationary and seasonal data; hence, the need for Seemingly Unrelated Regression (SUR) model to capture the correlated error terms inherent among the response variables. Thus, this study was aimed at modelling the nonstationary and seasonal space-time data using the GSTSARIMA-SUR model. The GSTSARIMA model was modified by incorporating a system of equations; SUR. The generalised least squares method was employed for model estimation, while the weighted mean was used as the weight of locations. The seasonal fractional long memory persistence approach was utilized in carrying out seasonality and stationarity tests with a seasonal AR(1). For the stationarity condition, d must lie between - 0.5 and 0.5, where d denotes the parameter that controls stationarity. For the significance of the t-test at 5% level, one-tailed test at t = 1.64 was used. The exploratory data analysis was carried out, and the model adequacy was established using the least Mean Square Error (MSE) values. The monthly rainfall and temperature datasets of the West African countries spanning January 1961 to December 2016 were used to validate the model. Sierra Leone had the highest rainfall value of 1108.60mm, while Mauritania had the lowest value of 63.03mm. Mali had the highest temperature value of 35.030C,while Cape Verde had the least: 26.560C. The MSE values were (6348.041, 0.799), (8961, 5.754), for the rainfall and temperature series for GSTSARIMA-SUR and GSTSARIMA models, respectively. Hence, the GSTSARIMA-SUR is more efficient in handling nonstationary and seasonal data in a system of equations.