New Statistical Test to Determine the Best Model for Forecasting Water Discharge Data: Tigris and Euphrates Rivers in Iraq as a Study Case

In this research, the time series were analysed for four gauges (Mosul, Baghdad, Kut, and Husayabah) using autoregressive (AR) models with constant and periodic autoregressive coefficients. It was found that the best model for Mosul, Baghdad, and Husaybah gauges is AR (2) with periodic autoregressive coefficients, while the best model for the Kut gauge was AR (2) with constant autoregressive coefficients. The test was also suggested to determine the most appropriate model based on the values of autocorrelation of residuals (independent normal variable) and it was compared with the drawings of correlograms of autocorrelation of residuals rk(ξ) and with two tests: the AIC test and the portmanteau lack test. It was concluded that the suggested test was more accurate and more reliable.